1) Problem #PRAFV6A "PRAFV6A - 167090 - For a random samp..." |
For a random sample size of n=250 resulted in x=176. Test the following at the .01 significance level. Ho: p=.60 HA: p<.60 Fail or reject? |
Multiple Choice:
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Hints: |
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2) Problem #PRAFWPC "PRAFWPC - 167588 - For a random samp..." |
A)
For a random sample size of n=165 resulted in x=58. Test the following at the .01 significance level. Ho: p=.40 HA: p≠.40 What is your final p-value for this problem? (write the full number) |
Algebraic Expression:
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Hints: |
.0951 x 2 = .1902 |
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B)
Reject or Fail to Reject? |
Multiple Choice:
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Hints: |
Therefore, you fail to reject the null. |
3) Problem #PRAFWPD "PRAFWPD - 167589 - For a random samp..." |
A)
For a random sample size of n=54 resulted in x=25. Test the following at the .01 significance level. Ho: p=.30 HA: p>.30 What is the final p-value for this problem? (write the whole number) |
Algebraic Expression:
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Hints: |
Since the alternative is greater than μ, you need to do 1 - the pvalue you find. 1 - .9948 = .0052 Type in .0052 |
B)
Reject or Fail to Reject? |
Multiple Choice:
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Hints: |
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4) Problem #PRAFWR2 "PRAFWR2 - 167671 - A random sample o..." |
A)
A random sample of size n=45 had a mean of 44 and a standard deviation s = 5.1. Test the following hypotheses at the .05 significance level. Ho: μ=43 HA: μ<43 What range does the p-value fall between? |
Multiple Choice:
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Hints: |
Tn-1 = x-μ / (s÷sq-rt of n) |
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B)
Reject or Fail to Reject the null? |
Multiple Choice:
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Hints: |
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5) Problem #PRAFWSZ "PRAFWSZ - 167701 - A random sample o..." |
A)
A random sample of size n=100 had a mean of 50 and a standard deviation s = 7. Test the following hypotheses at the .05 significance level. Ho: μ=48 HA: μ>48 What range does the p-value fall between? |
Multiple Choice:
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Hints: |
Tn-1 = x-μ / (s÷sq-rt of n) |
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B)
Reject or Fail to Reject the null? |
Multiple Choice:
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6) Problem #PRAFXNC "PRAFXNC - 168518 - A student thinks ..." |
A)
A student thinks Mr. Simoneau wears an average of 9 plaid shirts per week. However, Mr. Simoneau claims that he wears less than 9 plaid shirts per week. Over a 4 week period, it was observed that Mr. Simoneau wore 7.2 shirts per week, with a standard deviation of 2. What is the p-value for this problem? (include the whole number) |
Algebraic Expression:
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Hints: |
n = 4 x-bar = 7.2 standard deviation = 2 |
Answer is .0359 |
B)
Based on a .05 significance level, can we say that Mr. Simoneau's claim is true? |
Algebraic Expression:
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Hints: |
Therefore, Simoneau isn't a liar! |
7) Problem #PRAFXNR "PRAFXNR - 168530 - Wiz khalifa, Snoo..." |
A)
Wiz khalifa, Snoop Dogg and Eric Simoneau hang out an average of 360 days a year with a standard deviation of 4 days . Snoop dogg claims they in fact chill more than 360 days per year. Based on a study conducted by Eric's stalkers over the course of three years, they hang out 363 days. What is the p-value for this problem? (include the whole number) |
Algebraic Expression:
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Hints: |
Since it is greater than, you need to do 1 - the p-value you first get. |
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B)
Based on a .05 significance level, can we say that Snoop Dogg is correct?
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Multiple Choice:
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Hints: |
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8) Problem #PRAFXQG "PRAFXQG - 168584 - For a given probl..." |
A)
For a given problem, you have the following information: Ho: μ=52 HA: μ<52 σ = 2 n= 25 alpha = .05 Assume that μ = 50. What is the power of this problem? |
Algebraic Expression:
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Hints: |
Use the x-bar that you find to find the p-values for the assumed μ. The power would be the p-value if you reject the null (which you should do in this instance because we are assuming that μ = 50, therefore it's less than 52). |
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B)
What is the probability of making a Type II Error? |
Algebraic Expression:
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Hints: |
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9) Problem #PRAFXQY "PRAFXQY - 168599 - For a given pro..." |
A)
For a given problem, you have the following information:
Ho: μ=48 HA: μ<48 σ = 10 n=100 alpha = .01 Assume that μ = 46. What is the power of this problem? |
Algebraic Expression:
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Hints: |
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B)
What is the probability of making a Type II error? |
Algebraic Expression:
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Hints: |
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10) Problem #PRAFWKV "PRAFWKV - o known #2" |
Bob wanted to maximize the time that he can stay at home before heading off to school. He claims that he can get to school on time in an average of 20 minutes with a standard deviation of 3 minutes. Peter believes that Bob will take longer than he thought and be late for school. To test this claim, Bob timed how long it took to get to school for a 2 weeks and found that the average time he took was 22.1 minutes. Was Peter's assumption correct? Test at the .01 level. |
Multiple Choice:
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Hints: |
Ho: µ = 20 minutes Ha: µ > 20 minutes σ = 3 minutes n = 14 x-bar = 22.1 minutes alpha = .01 Since σ is known, we can solve by using the Z-score formula. Z = (x-bar - µ) / (σ/√n) |
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11) Problem #PRAFW77 "PRAFW77 - s known #1" |
A computer factory states that they can produce a computer in an average of 15 minutes. The factory implemented new technology in the hopes of seeing a shorter production time, so they decided to monitor the amount of time it took to make a computer. They monitored the production of 35 computers and got a mean production time of 13.5 minutes with a standard deviation of 5. Was the factory's effort to reduce production time successful? Test at the 0.05 level. |
Multiple Choice:
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Hints: |
Ho:µ=15 minutes Ha:µ<15 minutes n=35 s=5 minute x-bar=13.5 minute alpha=.05 Since σ is not known but s is, we have to use the tn-1 formula: tn-1 = (x-bar - µ) / (s/√n) |
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12) Problem #PRAFW83 "PRAFW83 - s known #2" |
Bob is trying to increase the time that he can remain underwater. He knows that the average time that he can remain under water is 3 minutes. Bob did more breathing exercises in hopes of increasing his time. In 15 trials, his average time under water was 5 minutes with a standard deviation of 2 minutes. Was Bob successful? Test at the .01 level. |
Multiple Choice:
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Hints: |
Ho: µ=3 Ha: µ>3 n=15 x-bar=5 minutes s=1 minute alpha=.01 Since we don't known σ but we know s, we will have to use the tn-1 formula: tn-1 = (x-bar - µ) / (s/√n) |
13) Problem #PRAFYAQ "PRAFYAQ - p #1" |
A company states that 40% of its employees receive a pay raise. An employee thinks that they are overstating their claim and decided to test it. Surveying 500 employees, 182 of them said that they received a raise. Was the employee right? Test at the 1% level. |
Multiple Choice:
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Hints: |
Ho: p=.4 Ha: p<.4 n=500 p-hat=182/500 alpha = .01 Since this is a proportion problem we will use the z-formula: Z = (p-hat - p) / (√((p-hat)(q))/n) *note - q is simply 1-(p-hat). |
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Ho: p=.4 Ha: p<.4 n=500 p-hat=182/500 Since this is a proportion problem we will use the z-formula: Z = (p-hat - p) / (√((p-hat)(q))/n) *note - q is simply 1-(p-hat). |
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14) Problem #PRAFYAR "PRAFYAR - p #2" |
Jim says that 80% of the kids at school ate school lunch. Bob doesn't believe this and thinks more than 80% of kids ate school lunch. He surveyed 200 kids and 174 of them said that they ate school lunch. Was Bob right? Test at the 1% level. |
Multiple Choice:
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Hints: |
Ho:p=.8 Ha:p>.80 n=200 p-hat=174/200 alpha=.01 Since this is a proportions problem, we can use the z-score formula: Z=(p-hat - p) / (√((p-hat)(q))/n) |
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15) Problem #PRAFYA3 "PRAFYA3 - Type Error #2" |
Using the information from the previous problem, calculate the probablility of Type II Error. Round to the hundredth's place. |
Algebraic Expression:
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Hints: |
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16) Problem #PRAFYA9 "PRAFYA9 - 169166 - Type Error #3" |
Given the following information: Ho: µ=5 Ha: µ>5 n=10 σ=.8 alpha = .05 Assume µ=6 Find the probability of Type II Error. Round answer to the nearest hundredths. |
Algebraic Expression:
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Hints: |
z = (x-bar - µ) / (σ/√n) The value of z in this equation will be the 1-significance level (.05). In this case it will be .95. Find the number on the z-table that .95 is closest to. In this case it is 1.65. Solving for x-bar, we get a value of 5.43. |
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17) Problem #PRAFXSP "PRAFXSP - 168652 - A teacher believe..." |
A teacher believes his students will score poorly on an exam. A sample of 28 test scores results in an average of x-bar = 78.2. There is a standard deviation of of 15.6 points. Find the p-value for the following hypothesis. Ho: µ = 80 Ha: µ < 80 |
Algebraic Expression:
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18) Problem #PRAFW8Z "PRAFW8Z - 168135 - Amy powers is tes..." |
A)
Amy powers is testing her third grade class. The class is composed of 23 students. She believes that all her stuedents should should recieve an 80%, if not better, on the test. The classes mean grade is an 82.6 with a standard deviation s=11.6. Test the two hypothesises at .10 significance. Find P-value. |
Algebraic Expression:
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B)
What is the outcome? |
Algebraic Expression:
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19) Problem #PRAFW8H "PRAFW8H - 168120 - The average hourl..." |
A)
The average hourly wage for a teenager working at a summercamp is $8.50 an hour wisth a standard deviation of $0.64. At Days in the Arts Summer camp, there was a sample size of 50 workers who who earned an avergae houly wage of $8.71. Test the claim that the avergae was not changed at a .05 significance level. First, find the P -value. |
Algebraic Expression:
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B)
You reject the Null in this problem. True or False? |
Algebraic Expression:
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20) Problem #PRAFWK3 "PRAFWK3 - 167517 - A company claims ..." |
A)
A company claims that the price of a new hot tub is less thab $3000. In a given study, the average price of a new hot tub is $3300. Out of a sample size of 10 hot tubs, there was a standard deviation of $600. Start testing the hypothesis at a 0.05 significance level by calculating the p-value. |
Algebraic Expression:
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B)
Now that you have succesfully calculated the p-value, do you reject of fail to reject the null? |
Algebraic Expression:
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C) |
Algebraic Expression: |
21) Problem #PRAFWKU "PRAFWKU - 167510 - Renee is selling ..." |
Renee is selling candycanes to help benefit her hockey team. For the 62 candy canes that she sells, the prices were Ho: µ = $1.00 and Ha: µ > $1.00. Test the hypothesis if the standard deviation is $0.40 and the significance level is .01. Calculate Type 1 Error. |
Algebraic Expression:
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22) Problem #PRAFWJ9 "PRAFWJ9 - 167492 - Cynthia is sellin..." |
Cynthia is selling used cars. For the sample size of 50 automobiles, the prices Ho: µ = 34,000 and Ha: µ >34,000. The standard deviation is 5,000. Test the hypothesis at .05 significance level. Calculate Type 1 Error. |
Algebraic Expression:
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23) Problem #PRAFWJX "PRAFWJX - 167482 - Nicco is conducti..." |
Nicco is conducting a survey for his senior class. Of the 286 people he asks, 157 of them respond positively. Test the folloing hypothesis at 0.01 significance in Ho: p = 0.60 and Ha: p < 0.60. |
Algebraic Expression:
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24) Problem #PRAFWDQ "PRAFWDQ - 167320 - A survey is condu..." |
A survey is conducted with a sample size of 300 people. Of those 300 people, 126 of them responded positively. Test the following at .01 signifigance level if Ho : p = 0.50 and p > 0.50. |
Algebraic Expression:
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25) Problem #PRAFWKN "PRAFWKN - 167504 - The mean weight o..." |
A)
The mean weight of a can of soda is supposed to be 12oz with standard deviation of 3oz. Matt checks 40 cans and decides to reject them because they are different from 12 oz at the 1% significance level when in fact it is 12 oz. What type of error is it? |
Multiple Choice:
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Hints: |
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B)
Reject H(null) if z<_______or >_______ when in fact μ=____? |
Exact Match (case sensitive):
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26) Problem #PRAFWDA "PRAFWDA - 167307 - A research compan..." |
A research company states that 80% of all Americans like to eat pie. Bobby decides to test this claim and conducts a survey of 2000 people of which 1567 say they like to eat pie. Is there sufficient evidence at the 0.05 level to conclude that the actual percentage is different from 80%? answer yes or no then comma(,) probability in decimal example: no, .5398 |
Algebraic Expression:
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Hints: |
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27) Problem #PRAFWKQ "PRAFWKQ - 167506 - Lizzy who is a ma..." |
Lizzy who is a manager of a factory decides that any sweater with a mean sleeve as far away from 2inches as 2.05 should be rejected. She inspected 20 sweaters with standard deviation of 2 inches. significance level 5%. What is the probability of a type II error? |
Algebraic Expression:
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Hints: |
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28) Problem #PRAFWKR "PRAFWKR - 167507 - A candy factory d..." |
A candy factory decides that any jelly beans with a mean length as far away from 2 cm as 2.1 should be rejected. A worker looks through 50 with standard deviation of 0.1cm. siginificance level of 5% Find the probability of a type II error. (answer in decimal) |
Algebraic Expression:
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Hints: |
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29) Problem #PRAFWJ4 "PRAFWJ4 - 167487 - A website states ..." |
A website states that Americans sleep an average of five hours. John surveys 10 people at school. The following is the hours they sleep: 8.5, 3.8,4.7,5.6,3.4,8.5,9.3,5.4,7.9,9.0 Does it appear that the website is true? Test at the 0.05 level. |
Algebraic Expression:
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Hints: |
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30) Problem #PRAFWD6 "PRAFWD6 - 167334 - In a small town o..." |
In a small town of a 1000 people, last year the number of people who used their credit card to buy groceries averaged 675 a day. The credit card company puts in effort to have more people use their credit card by implementing the reward system of accumulating points for a prize of the customers' choice. A year later. in a sample of 31 days, the number of people who use their credit card to purchase grocery averaged at 700 and standard deviation of 50. Test at the 0.05 level. |
Algebraic Expression:
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Hints: |
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31) Problem #PRAFWDT "PRAFWDT - 167323 - A health magazine..." |
A health magazine states that an average person drinks 2 cups of juice each day. Timmy who does not believe this and decides to ask 10 students in his school. Do the results of Timmy's survey support the magazine's claim at the 0.01 level? Data Timmy collected: (number of cups for each person) 4,1,5,2,3,1,1,6,2,3 answer format: reject or fail to reject and between which two numbers it fall? example: reject, between .70 and .80 |
Algebraic Expression:
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Hints: |
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32) Problem #PRAFWCW "PRAFWCW - 167295 - A pastery shop wa..." |
A pastery shop wants to purchase some fresh cherries from a farm if it is convinced that less than 5 percent have serious blemishes. The farmer examined 25 cherries and found out that 1 cherry had blemishes. Is there sufficient evidence at the 0.01 level to conclude that the cherries should be purchased? |
Multiple Choice:
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Hints: |
plug the given information into formula |
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33) Problem #PRAFWKM "PRAFWKM - 167503 - The mean number o..." |
A)
The mean number of chocolate chips in a certain type of ice cream is supposed to be 44 with standard deviation of 2. Tom looks over 80 cartons of ice cream and rejects all of them because it is different from 44 chocolate chips at the 5% significance level when in fact it is 44. What type of error is this? |
Algebraic Expression:
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Hints: |
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B)
Refer to previous problem. what is the condition to reject H(null) if z<_____or z>_______? |
Exact Match (case sensitive):
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Hints: |
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34) Problem #PRAFXRW "PRAFXRW - 168628 - Ron is tryin..." |
A)
Ron is trying to determine whether he should keep his ice cream shop on Hyde Park Ave or move it to Tremont St in Downtown for more business although there are more ice cream shops. He decides that if he has more than 74 customers in a week, he will remain in Hyde Park. After observing for a week, he uses a sample of 100 residents around his area, with a standard deviation of 10, and a significance level of 100. After a week of observing he finds that x-bar is 76.33, Assume that µ=78, find the Type II Error. What is the Z-score? |
Algebraic Expression:
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Hints: |
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B)
Using the z-score you found in the previous problem, what is the x-bar now? Round to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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C)
Using the previous information, find the Type II error. Round to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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D)
What happens if Ron makes a Type II Error? |
Multiple Choice:
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35) Problem #PRAFXNQ "PRAFXNQ - 168529 - Daisy is deb..." |
A)
Daisy is debating whether to close her botique next door to her hair salon at the Wrenthem Outlets. She is making her decision based on the number of visitors she has in a week, she believes that there are less than 264 people visiting and therefore she plans to close it. She decides to study a weeks worth of customers with a sample of 1000 customers at the outlet, and a standard deviation of 21.2. She find that x-bar is equal to 262.3 What is the Z-score? |
Algebraic Expression:
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Hints: |
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Fail to reject, means she should keep the boutique open. Cannot be determined, means you do not have enough information. Remember that in order to reject the null, p-value has to be less than the significance level. |
B)
Using the Z-score you found in the previous problem, find the p-value. Round to the nearest thousandth. |
Algebraic Expression:
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Hints: |
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C)
Using a significance level on .01, conclude whether she should close the store or not. |
Multiple Choice:
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36) Problem #PRAFXND "PRAFXND - 168519 - Bank of America&n..." |
A)
Bank of America has found that account holders use its card an average of 8.4 times per month. To increase usage, the company conducted a promotion for one month during which prizes could be won by using the card. During the promotion, a random sample of 28 account holders used the card an average of 9.7 times. The sample standard deviation was 2.6. What is the Z-score? Round to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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B)
Do these results provide sufficient evidence at the 0.05 level to conclude that card usage increased during the promotion period? Please actually tuype "fail to reject" or "reject", depending on your conclusion. |
Algebraic Expression:
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Hints: |
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37) Problem #PRAFV6F "PRAFV6F - 167095 - A group of 500 pe..." |
A)
A group of 500 people are tested to see if when placed with a sleeping deer they will choose to throw a rock at the deer and wake it up. The mean of the sample shows that 65% of the people WILL throw the rock at the sleeping deer. Is this enough evidence to conclude that people will throw the pebble at the deer more than 63% of the time at the .05 significance level? |
Multiple Choice:
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B)
At the .01 significance level? |
Multiple Choice:
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38) Problem #PRAFXQ7 "PRAFXQ7 - 168606 - A study is done t..." |
A study is done to determine how long the average text message is. 1000 texts are used to determine the answer. The conductor of the study guesses that the average text message is usually 60 characters long. The study shows that the average text message is 58 characters long, with a standard deviation of 19 characters. What is the z score for this example? |
Algebraic Expression:
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39) Problem #PRAFXRK "PRAFXRK - 168618 - A company claims ..." |
A)
A company claims that the percentage of animal parts in their products is less than 2. A group of vegetarians do a study, and in the products they tested they find that the percentage of animal parts is z=-2.31. Is this significant at the 5% level? |
Multiple Choice:
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B)
Is this significant at the 1% level? |
Multiple Choice:
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40) Problem #PRAFXRV "PRAFXRV - 168627 - The number of day..." |
A)
The number of days to recover from a cold are estimated to be less than 8.5. A test of 500 individuals finds that the sample mean is 8.2, with a standard deviation of 2 days. Are the results significant at 5% level? |
Multiple Choice:
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Hints: |
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B)
Are the results significant at the 1% level? |
Multiple Choice:
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41) Problem #PRAFXR7 "PRAFXR7 - 168637 - A math teacher be..." |
A math teacher believes that more than 80% of his students are passing his class, and comes to the conclusion that 87% are passing, so his hypothesis is right. However, he is wrong, and more than 30% of his students are failing. What type of error is this? |
Multiple Choice:
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42) Problem #PRAFXR4 "PRAFXR4 - 168634 - A grocer is looki..." |
A grocer is looking through a shipment of apples. He won't take a shipment in which more than 9% of the apples are seriously bruised. He concludes that less than 9% of the apples have bruises, but in fact he is wrong, and some of his customers are upset by the large number of bruised apples. Which type of error is this? |
Multiple Choice:
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43) Problem #PRAFXR9 "PRAFXR9 - 168639 - A doctor tests a ..." |
A doctor tests a sample of 50 patients for HIV. The population percentage of HIV patients is 12, and the doctor comes up with a result of 9. The sample's standard deviation is 6.5. What is the t-score of this study? |
Algebraic Expression:
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44) Problem #PRAFXSG "PRAFXSG - 168646 - Which statement i..." |
A)
Which statement is being tested in a significance test? |
Multiple Choice:
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B)
Which claim about the population are we trying to find evidence for? |
Multiple Choice:
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45) Problem #PRAFXSJ "PRAFXSJ - 168648 - The probability i..." |
The probability is computed assuming that H-null is |
Multiple Choice:
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46) Problem #PRAFW85 "PRAFW85 - 168139 - The average weigh..." |
A)
The average weight of cats in Boston is 10 pounds, with a standard deviation of 3. An animal shelter selects a sample of 20 cats and finds that the average weight is 8 pounds. Can you reject the mean? Find the p-value. Round to four decimal places. |
Algebraic Expression:
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B)
Can you reject the mean with a 0.05 significance level? |
Multiple Choice:
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47) Problem #PRAFWCT "PRAFWCT - 167292 - According to the ..." |
A)
According to the Daily Prophet, an average of 25 wizards were killed every month during Voldemort's reign of terror. To see if this is true, Harry Potter looked at the death records of 30 towns for August 1997, and found there was an average of 28 deaths. The standard deviation was 6 people. What is the p-value (after you subtract the upper and lower limits)? |
Algebraic Expression:
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B)
Do you reject or fail to reject at a significance of 0.05? |
Multiple Choice:
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48) Problem #PRAFWJ5 "PRAFWJ5 - 167488 - For a random samp..." |
A)
For a random sample of 200 observations, 71 successes were obtained. What is the z-score? Round to the nearest hundredth. H0: p = 0.40 HA: p < 0.40 |
Algebraic Expression:
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Hints: |
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B)
With a significance level of 5%, do you reject the null or fail to reject the null? |
Multiple Choice:
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49) Problem #PRAFBEZ "PRAFBEZ - 150062 - Arielle is taking..." |
A)
Arielle is taking a course in astronomy. Her mean test score is 87. The standard deviation is 6. What is the probability that she will get less than an 82 on her next test? Round to the nearest tenth. |
Algebraic Expression:
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Hints: |
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82 - 87 / 6 |
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B)
If you take a random sample of 5 of her tests, what is the probability that the mean will be less than 82? Round to the nearest hundredth. |
Algebraic Expression:
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Hints: |
s.d / √N to find the new s.d.. |
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C)
What is the probability that the test score mean is betwee 82 and 85? Type in every number you see on your calculator. |
Algebraic Expression:
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Hints: |
Use the equation: x - mean / s.d. for both situations. |
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50) Problem #PRAFBEY "PRAFBEY - 150061 - Lucky's Valentine..." |
A)
Lucky's Valentine's Day Company produces teddy bears with an average height of 12 inches. the standard deviation is 1. What is the probability that a selected teddy bear is less than 11.9 inches? Round to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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x - mean / standard deviation or: 11.9 - 12 / 1 |
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B)
Every month, a worker is chosen to do a test of a random sample of 20 randomly selected teddy bears. Find the probability that the mean will be less than 11.9 inches. Round to the nearest hundredth. |
Algebraic Expression:
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Hints: |
s.d. / √N |
Now, insert that as the standard deviation into the equation: x - mean / s.d. |
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51) Problem #PRAFWDU "PRAFWDU - 167324 - L'amour Limosine ..." |
A)
L'amour Limosine Company is very popular in the parish of Bon Temps. To ensure that their patrons have the best ride possible, they do monthly checks on the height of the tires. In a random sample of 20 limos, there was a mean x-bar of 32.6 and a standard deviation (s)of 4.7. With α at .05 and μ of 30... H0: μ = ??? |
Algebraic Expression:
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B)
Ha: μ> ????? |
Algebraic Expression:
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C)
Should they reject the null or fail to reject the null of this sample? |
Algebraic Expression:
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52) Problem #PRAFWJS "PRAFWJS - 167477 - For a sample of 1..." |
A)
For a sample of 15 dogs heights, xbar= 576 mm and s= 44 mm. With alpha= 0.01 test the following the hypothesis. H0=590 Ha ≠ 590 What is the sample standard deviation? |
Algebraic Expression:
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B)
For a sample of 15 dogs heights, xbar= 576 mm and s= 44 mm. With alpha= 0.01 test the following the hypothesis. H0=590 Ha ≠ 590 Would you reject the null or fail to reject the null? |
Algebraic Expression:
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53) Problem #PRAFWKP "PRAFWKP - 167505 - Mr Cool Guy the S..." |
A)
Mr Cool Guy the Stats Guy gave a makeup test to 5 of his students. The test was out of 20 points. What is the mean of this situation with test scores of: 15, 17, 16, 10, and 18? |
Algebraic Expression:
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B)
Is there enough evidence at the 0.05 level to cnclude that the mean of the sampled population exceeds 12? Yes or no? |
Algebraic Expression:
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54) Problem #PRAFWK2 "PRAFWK2 - 167516 - A scientist was o..." |
A)
A scientist was observing a new type of kitty litter and was seeing how sucessful it is in attracting cats to do their business. In 500 observations, 182 sucesses were obtained. With α=0.01, what does n equal? |
Algebraic Expression:
|
B)
A scientist was observing a new type of kitty litter and was seeing how sucessful it is in attracting cats to do their business. In 500 observations, 182 sucesses were obtained. With α=0.01, what does p hat equal? |
Algebraic Expression:
|
C)
A scientist was observing a new type of kitty litter and was seeing how sucessful it is in attracting cats to do their business. In 500 observations, 182 sucesses were obtained. With α=0.01, what does z equal? |
Algebraic Expression:
|
D)
A scientist was observing a new type of kitty litter and was seeing how sucessful it is in attracting cats to do their business. In 500 observations, 182 sucesses were obtained. With α=0.01, do you reject or fail to reject?? |
Algebraic Expression:
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55) Problem #PRAFW8G "PRAFW8G - 168119 - If we reject Ho w..." |
A)
If we reject Ho when Ho is actually true, what kind of error did you committ? "Type I Error" or "Type II Error"? |
Algebraic Expression:
|
B)
If you overestimate a stock is that a Type 1 Error or Type 2 Error? |
Multiple Choice:
|
C)
Alfred is the head designer of the new line of satchel bags by Gucci. Mary is deciding whether or not she should invest in this new line. Based on past sales, she can assume a normal distribution with σ=60 and a mean of 40. To test this, she uses a sample size of 1000 and wishes to test: Ho: μ=40 Ho:μ>40 Describe a type 1 error. |
Ungraded Open Response: |
D)
Describe a Type 2 error |
Ungraded Open Response: |
E)
Which type of error is more serious in this case? |
Algebraic Expression:
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F)
What is the probability of the Type one error? |
Algebraic Expression:
|
G)
What is the probability of Type 2 error? |
Algebraic Expression:
|
H)
α corresponds with which type error? |
Algebraic Expression:
|
I)
β corresponds with which type error? |
Algebraic Expression:
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56) Problem #PRAFW8Y "PRAFW8Y - Type ll error question's #1 & 2" |
A)
If Ho:μ= 6.7 and Ha‹ 6.7. μ represents the speed of NFL lineman in a 40 yard dash. Am NFL scout believes linemen 40 yard dash speed has increased when in fact it hasn't. Is this a type l error or type ll? |
Multiple Choice:
|
B)
Say for the given previous problem the probabilty of a type ll error for that alternative= 0.0877. What is the Power? (Remember the equation for power, 1-β) |
Algebraic Expression:
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57) Problem #PRAFW8N "PRAFW8N - Hypothesis test Proportion problem #2" |
880 random NFL players are conducted in a survey and asked if they think their team has a legitimate shot at winning the superbowl. 171 admitted that they believe there team DOESN'T have a shot at winning. Calculate the 95% interval for the population proportion. |
Algebraic Expression:
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58) Problem #PRAFW8E "PRAFW8E - Hypothesis test Proportion problem #1" |
Owner Bob Craft wants to see what percentage of fans are satisfied with Patriot Place at Gilette Stadium. He decides that he wants the estimate to be within 3% at a 95% confidence interval. We have no idea of the true prpoportion of satisfied fans so we decide to use p=*0.5 |
Multiple Choice:
|
59) Problem #PRAFWKW "PRAFWKW - 167512 - Hypothesis Test Z value 2 questions" |
A)
For a set of data showing the work equipment between NBA basketball teams Boston Celtics and Chicago Bulls there's a standard deviation of 60. There's no difference in the work equipment between the two teams so the µ= 0. This is the Ho, Ha says µ is NOT equal to 0. The sample mean for the data is 18 random players, and their results gave an xbar= 17. Find the P-value? |
Multiple Choice:
|
B)
For the last part of the problem,when calcuating the pvalue why is it the correct step to multiply the Z score obtained by 2? |
Algebraic Expression:
|
60) Problem #PRAFWEF "PRAFWEF - 167343 - Hypothesis Test T-value 2 questions" |
A)
It is said that a steay diet of shirmp will cause 18 year old athlete's to lose exactly 10 lbs. over 5 months. A random sample of 49 athletes was taken, giving an average weight loss over 5 months of 12.5 lbs. With S = 7 lbs. Let alpha = .02. What is the calculated value for testing the above hypothesis? |
Multiple Choice:
|
B)
It is said that a steay diet of shirmp will cause 18 year old athlete's to lose exactly 10 lbs. over 5 months. A random sample of 49 athletes was taken, giving an average weight loss over 5 months of 12.5 lbs. With S = 7 lbs. Let alpha = .02. What is the p-value for this problem |
Multiple Choice:
|
61) Problem #PRAFWCX "PRAFWCX - Type I Error" |
As the alpha level gets lower, whic error rate also gets lower? |
Algebraic Expression:
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62) Problem #PRAFWC7 "PRAFWC7 - Type I Error" |
If the null hypothesis is false, you cannot make which kind of error? |
Algebraic Expression:
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63) Problem #PRAFYPR "PRAFYPR - term 4 project #6" |
A type 1 error is always made when... |
Multiple Choice:
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64) Problem #PRAFYPS "PRAFYPS - term 4 project #7 " |
Type II error refers to... |
Multiple Choice:
|
65) Problem #PRAFXSA "PRAFXSA - term 4 project #3 " |
In hypothesis testing, which of the following statements are always true? I. The P-value is greater than the significance level. II. The P-value is computed from the significance level. III. The P-value is the parameter in the null hypothesis. IV. The P-value is a test statistic. V. The P-value is a probability. |
Multiple Choice:
|
66) Problem #PRAFXSC "PRAFXSC - term 4 project #4 " |
A)
An inventor has developed a new, energy-efficient lawn mower engine. He claims that the engine will run continuously for 5 hours (300 minutes) on a single gallon of regular gasoline. Suppose a simple random sample of 50 engines is tested. The engines run for an average of 295 minutes, with a standard deviation of 20 minutes. Test the null hypothesis that the mean run time is 300 minutes against the alternative hypothesis that the mean run time is not 300 minutes. Use a 0.05 level of significance. (Assume that run times for the population of engines are normally distributed.) What is the P-value? |
Algebraic Expression:
|
Hints: |
|
B)
Referring to the previous problem, do you fail to reject or reject the hypothesis? |
Multiple Choice:
|
67) Problem #PRAFYPM "PRAFYPM - term 4 project #5" |
A)
Bon Air Elementary School has 300 students. The principal of the school thinks that the average IQ of students at Bon Air is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students. Among the sampled students, the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01. State the null and alternative hypothesis. |
Ungraded Open Response:
|
B)
Referring to the last question, do you fail to reject or reject the hypothesis? |
Multiple Choice:
|
68) Problem #PRAFV6G "PRAFV6G - term 4 project #1" |
A)
From long experience with a process for manufacturing a juice beverage it is known that the yield is normally distributed with a mean of 500 and a standard deviation of 96 units . For a modified process the yield is 535 units for a sample of size 50. What does
H0µ equal? |
Algebraic Expression:
|
B)
Using the last problem, find z=-µ/(σ/√n). |
Algebraic Expression:
|
Hints: |
|
69) Problem #PRAFXR6 "PRAFXR6 - term 4 project #2" |
The lifetime of a certain brand of heat pump is known to be normally distributed with a standard deviation of 2. A sample of 6 heat pumps yielded the following observations 2.0 1.3 6.0 1.9 5.1 4 At a= .05 is there reason to believe that the mean life of the heat pumps is greater than 2? Find a 95% confidence interval. |
Algebraic Expression:
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Hints: |
|
70) Problem #PRAFYPQ "PRAFYPQ - Problem #169521" |
A)
An insurance company is reviewing its current policy rates. When originally setting the rates they believed that the average claim amount was $1,600. They are concerned that the true mean is actually higher than this, because they could potentially lose a lot of money. They randomly select 64 claims, and calculate a sample mean of $2,000. Assuming that the standard deviation of claims is $500, and set a = .05 |
Algebraic Expression:
|
B)
According to your previous answer do you reject or fail to reject the null? |
Multiple Choice:
|
71) Problem #PRAFYPT "PRAFYPT - 169524 - What is the diffe..." |
What is the difference between a one-tailed test and a two-tailed test? |
Ungraded Open Response: |
72) Problem #PRAFYPU "PRAFYPU - 169525 - In hypothesis tes..." |
In hypothesis testing, which of the following statements are always true? |
Multiple Choice:
|
73) Problem #PRAFYPV "PRAFYPV - 169526 - A company claims ..." |
A)
A company claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim,they surveyed 100 customers, using simple random sampling. 73 percent say they are very satisified. Based on these findings, can we reject the company's hypothesis that 80% of the customers are very satisfied? 0.05 level of significance. |
Multiple Choice:
|
B)
According to the previous problem what is the p-value of the data? |
Algebraic Expression:
|
74) Problem #PRAFYPW "PRAFYPW - 169527 - A teacher gives o..." |
A)
A teacher gives out a test. the teacher states that women did better on the test than men. To test this claim, they choose a a simple random sample of 100 women and 200 men from a population of 100,000 volunteers.
At the end of the study, 38% of the men passed the test; and 51% of the women passed the test. Based on these findings, can we conclude that the test was passed by more women than for men? Use a 0.01 level of significance. do we reject the null or do not reject the null? |
Multiple Choice:
|
B)
What is the Z-score and p-value? |
Multiple Choice:
|
75) Problem #PRAFYPY "PRAFYPY - 169529 - A School has..." |
A)
A School has 300 students. The principal of the school thinks that the average IQ of students is at least 110. To prove her point, she administers an IQ test to 20 randomly selected students. the average IQ is 108 with a standard deviation of 10. Based on these results, should the principal accept or reject her original hypothesis? Assume a significance level of 0.01. |
Algebraic Expression:
|
B)
according to the problem above what is the t-score of the data? |
Algebraic Expression:
|
76) Problem #PRAFWJQ "PRAFWJQ - 167475 - The NFL studies h..." |
A)
The NFL studies how far qbs can throw if x-bar=114.9 and s=9.3 for the distance thrown of the 27 qb's chosen. what is the standard error of the mean? round to the nearest tenth |
Algebraic Expression:
|
B) |
Algebraic Expression: |
C)
the nba charts how high centers can jump. In the table from testing the entries read .84+/-.01 and x-bar=.84, what was the sample standard deviation s for these measurements? round to the nearest hundreth |
Algebraic Expression:
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77) Problem #PRAFWC2 "PRAFWC2 - 167299 - HOW REAL IS THIS ..." |
HOW REAL IS THIS SHIT? |
Algebraic Expression:
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78) Problem #PRAFYP3 "PRAFYP3 - 169532 - Quart bottles of ..." |
Quart bottles of colt .45 malt liquor should contain at least 32 ounces. A sample of 22 cartons contained the following amounts in ounces. 31.5 32.2 31.9 31.8 31.7 31.5 31.6 32.4 31.6 31.8 32.2 32.1 31.8 31.6 32.0 31.6 31.7 32.0 31.5 31.9 31.8 31.5 Is there sufficient evidence at the 0.05 level to support the companies claim? |
Multiple Choice:
|
79) Problem #PRAFYP4 "PRAFYP4 - 169533 - The average cost ..." |
The average cost of a condom is 27.50 a sample of 50 condoms has an average cost of 29.30. the standard deviation of the sample is 5.00. Should the null be rejected at alpha=.05? |
Multiple Choice:
|
80) Problem #PRAFYP5 "PRAFYP5 - 169534 - You have an SRS o..." |
A)
You have an SRS of size n = 9 from a Normal distribution with Σ = 1. You wish to test H0: μ=0, Ha: μ > 0. You decide to reject Ho if x-bar > 0 and to acccept Ho otherwise. find the probablitity that the test rejects Ho wne in fact u = 0. round to the nearest tenth. |
Algebraic Expression:
|
B)
You have an SRS of size n = 9 from a Normal distribution with Σ = 1. You wish to test H0: μ=0, Ha: μ > 0. You decide to reject Ho if x-bar > 0 and to acccept Ho otherwise. Find the probablity of a type II error when μ=.3. round to the nearest tenth |
Algebraic Expression:
|
C)
You have an SRS of size n = 9 from a Normal distribution with Σ = 1. You wish to test H0: μ=0, Ha: μ > 0. You decide to reject Ho if x-bar > 0 and to acccept Ho otherwise. Find the probability of a type II error when μ=1. round to the nearest thousandth. |
Algebraic Expression:
|
81) Problem #PRAFS4B "PRAFS4B - 164146 - The NFL combine m..." |
The NFL combine measures many attributes of an athlete, a certain portion of the test ranks certain positions specific skills. The scores that can be achieved for a skills test ranges from a 1.00 to a 5.00. the scores of 17 quaterbacks had a symmetric distribution with x-bar=1.67 and s=0.25. give a 95% confidence interval for the mean score of the quarterbacks. |
Multiple Choice:
|
82) Problem #PRAFYP7 "PRAFYP7 - 169536 - A Type II error i..." |
A)
A Type II error is committed when we reject a null hypothesis that is true. type in true or false |
Algebraic Expression:
|
B)
µ = 17 is an appropriate null hypothesis. type true or false. |
Algebraic Expression:
|
83) Problem #PRAFYP2 "PRAFYP2 - 169531 - A company has cre..." |
A company has created an energy saving air conditioner that claims to have a life of 3,200 hours. Samples of eight ac's were tested and their lives in hours appear below. 3,675 3,597 3,412 3,976 2,831 3,597 3,211 3,725 Is there sufficient evidence at the 0.05 level to support the organizations claim? |
Multiple Choice:
|
84) Problem #PRAFYAT "PRAFYAT - 169152 - The CEO of a powe..." |
A)
The CEO of a powerful corporation that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, a reporter surveyed 100 customers, using simple random sampling. Among the sampled customers, 73 percent say they are very satisified. What is z? Round to the nearest hundredth. |
Algebraic Expression:
|
B) |
Algebraic Expression:
|
C)
Refer to the previous problem. Can we reject the CEO's hypothesis that 80% of the customers are satisfied? |
Multiple Choice:
|
85) Problem #PRAFS6F "PRAFS6F - 164212 - A quality control..." |
A)
A quality control official at a candy packaging facility wants to make sure that there is a mean amount of 22 candies per package. Of the 16 packages he checked, he found a sample mean of 18 with a standard deviation of 1. Is this data good enough evidence to prove that the facility is under-packaging the candy? Fill in the blank. X~N( , ). Type only ( , ). |
Algebraic Expression:
|
B)
Refer to the previous problem. What is Z? |
Algebraic Expression:
|
C)
Refer to the previous problem. What is the p value? |
Algebraic Expression:
|
D)
If the alpha is .05, what should the conclusion be, reject or fail to reject? |
Multiple Choice:
|
86) Problem #PRAFS6H "PRAFS6H - 164214 - To sew a certain ..." |
A)
To sew a certain fabric, needles with a diameter of 2mm are needed, so a seamstress buys a package of 50 needles claiming to have diameters of 2mm. If the needles are too large the fabric will tear, but if they are too small, the seamstress cannot thread the needle. The seamstress examines half of the 50 needles and finds that they have a sample mean diameter of 2.02 and a standard deviation of .07. Will the needles work? First, fill in the blank. x bar~N( , ). type only ( , ). |
Algebraic Expression:
|
B)
Refer to the previous problem. What is Z? round to the nearest hundredth. |
Algebraic Expression:
|
C)
Refer to the previous problem. What is the p value? |
Algebraic Expression:
|
Hints: |
|
D)
Refer to the previous problem. Do we reject or fail to reject the null? |
Multiple Choice:
|
87) Problem #PRAFW8R "PRAFW8R - 168127 - A researcher beli..." |
A)
A researcher believes that
in recent years women have been getting taller. She knows that 10 years ago the
average height of young adult women living in her city was 63 inches. The
standard deviation is unknown. She randomly samples eight young adult women
currently residing in her city and measures their heights. The following data
are obtained: [64, 66, 68, 60, 62, 65, 66, 63.] α= .05 What is t? Round to the nearest hundredth |
Algebraic Expression:
|
Hints: |
t = X −μ0 = 64.25−63 =1.387 sX 0.901 |
B)
Refer to the previous problem. What is the p-value? round to the nearest 3rd decimal place. |
Algebraic Expression:
|
C)
Refer to the previous problems? Should the researcher reject the null or fail to reject? |
Multiple Choice:
|
D)
Refer to the previous problem. What is the probability of Type 1 error occurring? |
Algebraic Expression:
|
Hints: |
|
E)
Refer to the previous problem. At what value on the density curve would the researcher be able to reject the null hypothesis? Round to the nearest hundredth. |
Algebraic Expression:
|
Hints: |
|
F)
Refer to the previous problems If the researcher did reject the null hypothesis, but the actual mean was less than 64.49, what type of error would that be? |
Multiple Choice:
|
88) Problem #PRAFXX5 "PRAFXX5 - 168821 - A High School stu..." |
A)
A High School student playing basketball wants to know how many people of the next random 50 people who walk down the street next to his court can make a basket. His friend believes half the people will make it (the null hypothesis). What is the proportion of people who make the basket? |
Algebraic Expression:
|
B)
Refer to the previous problem. What is the P value? |
Algebraic Expression:
|
C)
Refer to the previous problem. Based on an α of .05, can we reject the null hypothesis, yes or no? |
Multiple Choice:
|
89) Problem #PRAFYP6 "PRAFYP6 - 169535 - Hyp Test #3+4" |
A)
A t-shirt manufacturer is investigating a type of cotton, which has a standard deviation of 0.3. The company wishes to test the hypothesis H0: μ = 14 against HA: μ < 14, using a random sample of 16 shirts. Find β if the actual mean is 13.0. |
Algebraic Expression:
|
B)
What is the power given the situation in the above problem? |
Algebraic Expression:
|
90) Problem #PRAFYP8 "PRAFYP8 - Hyp Test #6+7" |
A)
The mean SAT math score in a school district is 430. A group of 60 randomly selected students are put into a special SAT course, and their mean score is 462 with a standard deviation of 120. Find the critical value, round to the nearest thousandth. |
Algebraic Expression:
|
B)
Which is the correct conclusion? |
Multiple Choice:
|
91) Problem #PRAFYP9 "PRAFYP9 - Hyp Test 8+9" |
A)
A sales pitch has a 60% success rate, a new approach is tried. Out of 100 people, there are 75 sales. H0 : p=0.6 HA : p>0.6 What is the critical value for a=.5, round to the nearest hundredth. |
Algebraic Expression:
|
B)
What is the critical value for a = 1%, round to the nearest thousdandth. |
Algebraic Expression:
|
92) Problem #PRAFWJT "PRAFWJT - 167478 - Hyp Test #1+2 " |
A)
AT&T believes that the proportion of households that have 4 cell phones is 30%, but suppose Verizon suspects that the proportion of households that have 4 cell phones is not 30%. Before Verizon makes a commercial calling out AT&T, they decide to conduct a hypothesis test, they survey 150 households and find that 43 of the surveyed households have 4 cell phones. Given : HA: p=.30 HO: ≠ .30 What is the distribution for the hypothesis test? |
Algebraic Expression:
|
B)
Which of the following is correct (assuming that α = .5)? |
Multiple Choice:
|
93) Problem #PRAFXSS "PRAFXSS - 168655 - Hyp Test #5" |
In past the standardized test scores at a certain school district have varied normally with a μ=76 and σ = 8.4. Carry out a test of significance for : HO:μ = 76 HA:μ > 76 If a student's average score is 95, is this significant at the 5% level? |
Multiple Choice:
|
94) Problem #PRAFWR7 "PRAFWR7 - Hypothesis Tests 4" |
Carrie is applying to college. She really wants to go to Jungle Gym University in Maine. She's heard that an average of 48 applicants from her state are admitted into the University per year. However, Carrie is pessimistic about her chances and feels that the school admits less than 48 students from her home state per year. If they admit more than 48 students, she will apply. If not, then she won't. Assume the following: σ=10 N=100 α= 0.01 **μ=46** Find the probability of Carrie making a type II error, or applying to Jungle Gym University even though they admit less than 48 students. |
Algebraic Expression:
|
Hints: |
|
|
Power= 1-P (type II) = 1- 0.37 = 0.63 |
95) Problem #PRAFV6Q "PRAFV6Q - 167103 - Hypothesis Tests 2 and 3" |
A)
Alice wants to know if all white rabbits have issues with punctuality. The Mad Hatter tells Alice that white rabbits on average run 27.5 minutes late. However, Alice does not have faith in him and decides to test it. She asks 50 white rabbits in Wonderland how late they typically are and finds that the average tardiness of these 50 rabbits is 29.3 minutes, with a σ of 5 minutes. Considering an alpha of 0.05, determine the hypotheses of Alice's experment. What is the null hypothesis? |
Algebraic Expression:
|
Hints: |
|
B)
Revert back to the previous problem, which states that Alice's data is as follows: μ=27.5 minutes Ν=50 white rabbits (x-bar)=29.4 minutes σ= 5 minutes What is the p-value of this data? |
Algebraic Expression:
|
Hints: |
|
-------------- (5/√50) Z= 29.3-27.5 -------------- 0.71 Z= 2.54 |
1-0.9945, which is 0.0055. We'd reject this null, since 0.0055<0.05 |
96) Problem #PRAFXQX "PRAFXQX - Hypothesis Tests 6" |
Josh wants to know how many doughnuts he can eat before he starts to feel sick. He asks 12 of his buddies to help him conduct an experiment (they obviously agree, since it means they receive free doughnuts). He wants to find the 95% confidence interval for the data he collected, which is shown below: (x-bar)= 4.49 s =0.83 |
Algebraic Expression:
|
Hints: |
Since we do not know σ yet we do know s, we use the t-table. |
standard error = (s/√n) = (0.83/√12) = 0.24 The confidence interval can be determined by using the following equations: (x-bar)-tn-1 x (s/√n) (x-bar)+tn-1 x (s/√n) 4.49-(2.201) x (0.83/√12) 4.49+ (2.201) x (0.83/√12) 4.49 -(2.201 x 0.24) 4.49+ (2.201 x 0.24) 3.963 to 5.017 |
(____, ____) |
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97) Problem #PRAFV6C "PRAFV6C - Hypothesis Tests 1" |
What is the difference between the hypothesis test: and the test: ? |
Multiple Choice:
|
98) Problem #PRAFXSB "PRAFXSB - Hypothesis Tests 7" |
Ian McGregor has a scottish terrier. He is wondering if his dog is a healthy weight, so he does some research. One of his sources says that the average weight of a terrier is 15 pounds. Ian however, thinks his dog weighs less than that. Find the probability that Ian makes a type II error. Assume the following information: μ=14 σ=10 n=100 α= 0.01 |
Algebraic Expression:
|
Hints: |
H0: μ=15 HA: μ<15 |
Since the alpha is 0.01, look this value up on the z-table to find the corresponding z-score, which is -2.33. Plug this into the equation: z= (x-bar)-μ -------------- (10/√100) -2.33= (x-bar) -15 ---------------- 1 (x-bar)= 12.67 |
|
z=12.67-14 ------------ 1 z=-1.33, which corresponds to 0.092 when you look at the z-table. |
=1-0.092 = 0.908 |
99) Problem #PRAFYA5 "PRAFYA5 - 169162 - Hypothesis Tests 9 and 10" |
A)
The owner of a large clothing store chain claims that 80 percent of her 1,000,000 customers are satisfied with the clothing they've purchased and the service they received from the store's employees. Alan is a disgrunted customer. He wants to test this claim. He surveyed 100 random customers. Among the sampled customers, 73 percent say they are satisified. Based on these findings, can Alan prove that the store owner was wrong? Can he reject the hypothesis that 80% of the customers are satisfied? Use a 0.05 level of significance. |
Algebraic Expression:
|
Hints: |
H0: P = 0.80 HA: P ≠ 0.80 |
σ = √[ P * ( 1 - P ) / n ] = √[(0.8 * 0.2) / 100] = √(0.0016) = 0.04 |
z = ((p-hat) - P) / σ = (.73 - .80)/0.04 = -1.75 -1.75>z>1.75, seeing as it's a two-tailed test (≠ as opposed to < or >) Now find P(z < -1.75) and P(z > 1.75). =0.04 =0.04 The P-value = 0.04 + 0.04 = 0.08. |
p>α 0.08>0.05 which means we fail to reject the null. Alan cannot prove that the store owner was wrong. Type "No" into the answer box. |
B)
The same clothing store owner makes another claim several weeks later, that at least 80 percent of her 1,000,000 customers are satisfied with the clothing and the service. Alan is still upset at the store, and wants to try to disprove this new statement. He surveys 100 random customers again, and 73 percent say that they are content. Based on these findings, should Alan accept or reject the store owner's hypothesis? Assume a significance level of 0.05. |
Algebraic Expression:
|
Hints: |
H0: P ≥ 0.80 HA: P < 0.80 |
σ = √[ P * ( 1 - P ) / n ] = √[(0.8 * 0.2) / 100] = √(0.0016) = 0.04
|
Step 3: Calculate the z-score and the p-value. z = ((p-hat) - P) / σ = (.73 - .80)/0.04 = -1.75
After looking up -1.75 on the z-table, you can see that the p-value = 0.04. |
|
100) Problem #PRAFXQH "PRAFXQH - Hypothesis Tests 5" |
UMass Amherst is trying to encourage their students to stop driving to campus. The University claims that on average it takes 30 minutes to find a parking spot on campus. Ashley doesn't believe that it takes that long to find a parking spot, and keeps track of the data regarding her next five times driving to campus. She calculates x=20 minutes. Assuming that the time it takes to find a parking space is normal, and that σ= 6 minutes, perform a hypothesis test of Ashley's claim with an alpha of 0.10. Do we reject or fail to reject? |
Algebraic Expression:
|
Hints: |
The first step is to determine the null and aiternative hypotheses:
H0 : µ = 30 Ha : µ < 30 |
Next, calculate the test statistic:
z= 20-30 ----------
(6/ √5)
z= -3.727
Thus when you do out the graph, the point that contains the .10 to its left is at z=-1.28
|
Lastly, we can see that −3.727 < −1.28. So the test statistic is in the rejection region and we reject
the null hypothesis in favor of Ashley's alternative. |
101) Problem #PRAFXR3 "PRAFXR3 - 168633 - The federal gover..." |
A)
The federal government sent out 800 copies of the Census to a rural area in Montana. 496 were returned. Given the null hypothesis is 0.60, and the alternative hypothesis isn't 0.60, what is p-hat? |
Algebraic Expression:
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Hints: |
p-hat=496/800 p-hat=0.62 |
B)
What is q? |
Algebraic Expression:
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C)
What is the z? |
Algebraic Expression:
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Hints: |
Z=1.17 |
D)
What is the p-value? |
Algebraic Expression:
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Hints: |
1-.8790=.242 .242*2=.484 |
E)
Finally, test the hypothesis at alpha=0.05. |
Multiple Choice:
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102) Problem #PRAFYQC "PRAFYQC - 169541 - A shoe store is t..." |
A)
A shoe store is trying to see what sizes their customers are in order to have more of that size in stock. 100 women were surveyed, and 50 were a size 8. Assume the standard deviation is 10, and alpha is .05. What is x-bar? Round to the nearest thousandth. |
Algebraic Expression:
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Hints: |
Z-score=1.645 |
x-bar=51.645 |
B) |
Algebraic Expression: |
103) Problem #PRAFV6M "PRAFV6M - 4project_1" |
The __-value is the probability of observing a sample statistic as extreme as the test statistic, assuming the null hypotheis is true. |
Exact Match (case sensitive):
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104) Problem #PRAFXNE "PRAFXNE - 4Term_3" |
In hypothesis testing, which of the following statements are always true? I. The P-value is greater than the significance level. II. The P-value is computed from the significance level. III. The P-value is the parameter in the null hypothesis. IV. The P-value is a test statistic. V. The P-value is a probability. |
Multiple Choice:
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105) Problem #PRAFXNS "PRAFXNS - 4project_6" |
In the formula to solve z, z = ? |
Multiple Choice:
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107) Problem #PRAFWJ2 "PRAFWJ2 - 167485 - To test H(o): MU=..." |
To test H(o): MU=20 vs. H(A):MU not= 20, a sample of 400 is taken from a large population whose standard deviation is 5. H(o) will be rejected if xbar is greater than 20.5 or less than19.5. The level of significance =? round to hundreths place |
Algebraic Expression:
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Hints: |
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108) Problem #PRAFYQW "PRAFYQW - 169558 - Not rejecting the..." |
Not rejecting the null hypothesis when the alternative is true refers to a type (____) error. I or II? |
Algebraic Expression:
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Hints: |
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109) Problem #PRAFYQY "PRAFYQY - 169560 - 16 one acre plots..." |
16 one acre plots of wheat are harvested. Their average yield was found to be 701 bushels, and their standard deviation was 50 bushels. Due to the fact that last years harvest was 680 bushels on average per acre we want to test H(O):MU<=680 against H(A): MU>680 at alpha .05. Based on the above data should we reject or fail to reject the null. |
Algebraic Expression:
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Hints: |
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110) Problem #PRAFYAU "PRAFYAU - 169153 - It is desired tha..." |
It is desired that a weight loss pill will cause the user to lose exactly 10 lbs over 5 months. A random sample of 49 people was taken yielding an average weight loss over 5 months to be 12.5lbs with S=7lbs and Alpha =.02. What is the calculated value suitable for testing the above hypothesis. round to tenths place |
Algebraic Expression:
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Hints: |
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111) Problem #PRAFYA8 "PRAFYA8 - 169165 - The level of sign..." |
The level of significance is..... |
Check All That Apply:
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112) Problem #PRAFYQ2 "PRAFYQ2 - 169562 - The critical valu..." |
The critical value of a test statistic is determined from? |
Algebraic Expression:
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Hints: |
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113) Problem #PRAFYQH "PRAFYQH - 169546 - Word on the stree..." |
Word on the street is that an average of 28 trees were cut down yesterday in northern Massachusetts. I am writing a paper on the Weeping Willow and wish to confirm this piece of information, and so I look up this info for 16 different cities in norther MA and learn that an average of 25 trees were cut down yesterday. The standard deviation is 6. What is the p-value? |
Algebraic Expression:
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Hints: |
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Hints: |
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114) Problem #PRAFYQM "PRAFYQM - 169549 - Somewhere out the..." |
Somewhere out there, there is an official random sample of 125 observations, and 46 successes are obtained. Tell me the z-score! Please round to the nearest hundredth. H0: p =.3 |
Algebraic Expression:
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Hints: |
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115) Problem #PRAFYQP "PRAFYQP - 169551 - In the year 2038,..." |
In the year 2038, the average age at death is 175 with a standard deviation of 8. I travel to this time in a lovely time machine and in order to further understand their ways of life and how old they live to be, I ask 25 people their ages and the average answer I recieve is 169. Give the z-score, round to two decimal places. |
Algebraic Expression:
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Hints: |
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116) Problem #PRAFYQS "PRAFYQS - 169554 - There is a sample..." |
There is a sample of 50 dogs, and out of these 50, 15 have spots. Give me the z-score for this situation. H0: p =.2 HA: p <.2 |
Algebraic Expression:
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Hints: |
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117) Problem #PRAFYQV "PRAFYQV - 169557 - What is a Type I ..." |
What is a Type I error? |
Multiple Choice:
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118) Problem #PRAFYQZ "PRAFYQZ - 169561 - The mean sugar co..." |
The mean sugar content of Gramp's 38-layer cake is is supposed to be 2 miligrams, but each time he makes it, this tends to vary by .1 miligrams. Every time one is finished, Gramma tastes it to make sure that it is delicious. Gramma takes 50 bites every time. Using her wisdom, she can figure out the mean sugar content in each bite. Gramma will reject the cake if the mean sugar content is significantly different from 2 mg at the 5% significance level. This is a test of the hypotheses H0: Mu EQUALS 2. HA: Mu DOES NOT EQUAL 2. What is the probabiliy of a Type II error? Round to four decimal places. |
Algebraic Expression:
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Hints: |
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119) Problem #PRAFYQ5 "PRAFYQ5 - 169565 - You are holding i..." |
You are holding in your very hands the test results of 840 young, fresh Stats students. You plan to test hypotheses about the mean score (On this test, the number of possible points if 300), H0: mu EQUALS 275. HA: mu IS LESS THAN 275. at the 1% significance level. The population standard deviation is 60. What is the probability of a Type I error? |
Algebraic Expression:
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Hints: |
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120) Problem #PRAFV9S "PRAFV9S - 167198 - A random sample o..." |
A random sample of 20 Rohirrim had a mean of 32.6 horses and a standard deviation of 4.7. Test the following hypotheses at the 0.05 significance level. H0: μ=30 Ha: μ>30 |
Ungraded Open Response: |
121) Problem #PRAFWQA "PRAFWQA - 167617 - (3) TYPE I OR II ..." |
A)
(3) TYPE I OR II Aragorn wants to see if the redesign of the cover of a mail-order catalog for Ethril Swords will increase sales. A very large number of soldiers will recieve the original catalog, and a random sample of soldiers will recieve the one with the new cover. Based on past sales, Aragorn is willing to assume that the sales from the new catalog will follow a Normal distribution with σ=60 dollars and that the mean for the original catalog will be μ=40 dollars. Aragorn decides to use a sample size of n=1000. Aragorn wishes to test at the 0.01 significance level: H0: μ=40 Ha: μ>40 Describe a Type I error in this setting and the consequences of making a Type I error. |
Ungraded Open Response: |
B)
Descirbe a Type II error in this setting and the consequences of making a Type II error. |
Ungraded Open Response: |
C)
Which type of error is more serious in this case? |
Multiple Choice:
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122) Problem #PRAFWPB "PRAFWPB - 167587 - TYPE I ERROR If w..." |
TYPE I ERROR If we reject H0 when H0 is actually true, we have commited a _________ |
Multiple Choice:
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123) Problem #PRAFXQZ "PRAFXQZ - 168600 - (2) Sauron often ..." |
A)
(2) Sauron often uses experiments to measure how long an orc takes to find their way through a maze. The mean time is 18 seconds for one particular maze. Sauron thinks that a fire will cause the orcs to comlete the maze faster. He measures how long each of 10 orcs takes with a fire as a stimulus. What is the null hypothesis? H0=μ=? |
Multiple Choice:
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B)
What is the alternative hypothesis? Ha=μ |
Multiple Choice:
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124) Problem #PRAFXQ2 "PRAFXQ2 - 168601 - An Elvish company..." |
An Elvish company advertises that it deliver bow and arrows within 15 days of your purchase. A sample of 49 customers is taken. The average delivery time in the sample was 16.2 with a standard deviation of 5.6 days. Using a P-value, test the hypothesis at the 5% level of significance. |
Multiple Choice:
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125) Problem #PRAFWR8 "PRAFWR8 - 167677 - (3) TYPE I AND II..." |
A)
(3) TYPE I AND II The King of Rohan is thinking about strategically building a army base from which to attack Sauron. From what he found out from his spies, he knows that the mean number of gold that the people living near the base must have is over 80,000 to support this type of army base. The King decides to take a simple random sample of 50 people living near one potential location. Based on the mean population of this sample, the king will decide whether to build the base there. A number of similiar studies have shown that σ=5000 gold. What is the appropriate null hypothesis? |
Multiple Choice:
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B)
What is the appropriate alternative hypothesis? |
Multiple Choice:
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C)
Describe the two types of errors that you might make. |
Ungraded Open Response: |
126) Problem #PRAFXQ3 "PRAFXQ3 - 168602 - The amount of hum..." |
The amount of humans orcs can kill are normally distributed with μ=50 and s=6. Sauron suspects that the amount of humans that his orcs can kill is way above the average. These orcs are tested to see how many they can kill in a battlefield; the mean is 54.5 and the number of orcs=16. Conduct a hypothesis test with a significance level of 5%. |
Multiple Choice:
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127) Problem #PRAFXQ4 "PRAFXQ4 - 168603 - An elvish store t..." |
An elvish store tells prospective elvish soldiers that the average cost of it's bows and arrows is 52 gold with a standard deviation of 4.5 gold. A group of smart goblins thinks that the average cost is higher. In order to test the store's claim against their alternative, the students will select a random sample of size 100. Assume that the mean from their random sample is 52.8 gold. Perform a hypothesis test at the 5% level of significance. |
Multiple Choice:
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128) Problem #PRAFXRG "PRAFXRG - 168615 - Burger King ..." |
A)
Burger King claims that less than 5% of its chicken is served uncooked. If 2000 chicken sandwiches are randomly sampled and it is found that 75 have uncooked chicken. Does the result provide at the 10% evidence to conclude that more than 5% of their chicken is uncooked. |
Multiple Choice:
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B)
If that same test is run again and 140 chicken sandwiches are found to be uncooked is that then reason to suspect that more than 5% are uncooked? |
Multiple Choice:
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129) Problem #PRAFXRX "PRAFXRX - 168629 - A taxi company cl..." |
A)
A taxi company claims to be able to arrive at any destination in Boston in forty five minutes. A survey of 25 random taxi rides found that the average ride was 47 minutes long with a standard deviation of 15 minutes. Decide whether or not the claim is accurate at the 5% level. |
Multiple Choice:
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B)
Test that same claim with a standard deviation of 1 minute. |
Multiple Choice:
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130) Problem #PRAFXRY "PRAFXRY - 168630 - In the town of&nb..." |
A)
In the town of Rueens the average person makes 55,000 a year. An anthropologist visits town to see if the people are actually much wealthier. He asks and learns the following personal incomes: 49,000 50,000 50,000 53,000 53,500 53,700 54,000 54,500 54,700 54,800 54,900 55,000 56,000 57,000 57,000 58,000 59,000 60,000 61,000 62,000 63,000 64,000 65,000 66,000 67,000. At the 95% confidence level what is your conclusion? |
Multiple Choice:
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B)
What about at the 99% confidence level? |
Multiple Choice:
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131) Problem #PRAFXR2 "PRAFXR2 - 168632 - McDonalds claims ..." |
A)
McDonalds claims that less than 4% of its meat is served uncooked. If 1000 hamburgers are randomly sampled and it is found that 73 have uncooked meat. Does the result provide at the 5% evidence to conclude that more than 4% of their meat is uncooked. |
Multiple Choice:
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B)
If that same test is run again and 135 hamburgers are found to be uncooked is that then reason to suspect that more than 5% are undercooked? |
Multiple Choice:
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132) Problem #PRAFXRP "PRAFXRP - 168621 - In the town of Gr..." |
A)
In the town of Greensboro the average person makes 60,000 a year. An anthropologist visits town to see if the people are actually much wealthier. He asks and learns the following personal incomes: 54,000 55,000 55,000 58,000 58,500 58,700 59,000 59,500 59,700 59,800 59,900 60,000 61,000 62,000 62,000 63,000 64,000 65,000 66,000 67,000 68,000 69,000 70,000 71,000 72,000. At the 95% confidence level what is your conclusion? |
Multiple Choice:
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B)
What about at the 99% confidence level? |
Multiple Choice:
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133) Problem #PRAFXRD "PRAFXRD - 168612 - A horse-drawn car..." |
A)
A horse-drawn carriage company claims to be able to arrive at any destination in Boston in forty five minutes. A survey of 26 random horse-drawn carriage rides found that the average ride was 49 minutes long with a standard deviation of 16 minutes. Decide whether or not the claim is accurate at the 6% level. |
Multiple Choice:
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B)
Test the same claim with the standard deviation of 2 minutes. |
Multiple Choice:
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134) Problem #PRAFXRT "PRAFXRT - 168625 - You fail to rejec..." |
A)
You fail to reject even though you should have rejected? |
Multiple Choice:
|
B)
You reject when you should have failed to reject? |
Multiple Choice:
|
C)
Your test results say reject the null. If you do what type of error is that? |
Multiple Choice:
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D)
You fail to reject when the null is true. |
Multiple Choice:
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135) Problem #PRAFY2Q "PRAFY2Q - 169862 - In the criminal j..." |
In the criminal justice system, some crimes that are committed are considered especially heinous. In the Simibro justice system, anything is possible so there seems to be no system...these are his stories (DUN DUN): It's a typical day in the great class of Simibro and everyone is having fun. The classic red cups are on the desk for when a student needs help with a problem. Sometimes students have too much fun, and one of them decided to slap a cup across the room and hit Mr. Simibro in the back of the head. He didn't own up to it, and blamed it on the student next to him while that student did the same thing back. Since he was too confused to make a decision, the guity student was let off free with no punishment. What is this an example of? |
Multiple Choice:
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136) Problem #PRAFV57 "PRAFV57 - 167087 - A random sample o..." |
A random sample of size n = 34 had a sample mean(x-bar) of 992 and a standard deviation s = 7.2. Test the following hypotheses at the 0.05 significance level. Ho: µ = 990 Ha: µ ≠ 990 Between which range does your p-value fall? |
Multiple Choice:
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137) Problem #PRAFWR4 "PRAFWR4 - 167673 - A random sample o..." |
A random sample of n = 66 had a mean x-bar = 50.3 and a standard deviation s = 4.3. Test the following hypotheses at the 0.05 significance level. Ho: µ = 49 Ha: µ ≠ 49 Between which range does your p-value fall? |
Multiple Choice:
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