1) Problem #PRAFJ89 "PRAFJ89 - 157572 - Confidence Intervals - Notes - Proportions - Sample Size Calculations - EJS" |
To calculate the minimum sample size needed for an interval estimate of a population proportion, use the following information: Margin of Error = If you are seeking a certain magin of error, you can use the above formula to solve for n. Remember, if you want to control the size of your confidence interval, you can do this by controling your sample size. Hints: 1. If an estimate for p-hat is available, use that to estimate n. 2) If an estimate for p-hat is not given, use 0.5. 3) Using basic Algebra, solve for n, then round up - always. Make sure you copy this information into your notebook for future reference. © STATS4STEM.ORG |
Multiple Choice:
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2) Problem #PRAFJ88 "PRAFJ88 - 157571 - Confidence Intervals - Introduction Notes - Proportions- EJS" |
To create a confidence interval for proportions, we need to use the following formula: To use this formula, the following conditions must be met: Please make sure that this information is copied into your notebook for future reference! © STATS4STEM.ORG |
Multiple Choice:
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3) Problem #PRAFJ87 "PRAFJ87 - Confidence Intervals - Proportions - Sample Size" |
How large a sample should be surveyed to estimate the true proportion of college students who like to drink coffee, using a 95% confidence interval, if the researcher wishes to have a margin of error of just 3%? Link to t-table © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
m = 0.03 z* = 1.96 |
Answer: 1068 (ALWAYS ROUND UP FOR SAMPLE SIZE CALCULATIONS) |
4) Problem #PRAFJ86 "PRAFJ86 - 157568 - Confidence intervals - proportions - sample size" |
A)
A researcher wishes to estimate the proportion of adults who don't have a TV in their houses. How large a sample should be taken if the researcher wants to be 90% confident that her estimate is within 5% of the true proportion? To answer this question, include the fact that results from a prior survey of 300 adults showed that 30 adults didn't have a TV in their house? Link to t-table © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
If no estimate of the sample proportion is available, how large should the sample be? |
Algebraic Expression:
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Hints: |
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5) Problem #PRAFJ85 "PRAFJ85 - 157568 - Confidence intervals - proportions - sample size" |
A)
A medical researcher wishes to determine the percentage of adults who, on average, walk more than 1 mile per day. How lage should the sample size be if the researcher wishes to be 99% confident that the estimate is within 2 percentage points of the true proportion. For your calculation, use the information from a prior survey of 200 adults that showed that 25% of of the adults indicated that they walk, on average, more than 1 mile per day. Link to t-table © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
b) If no estimate of the sample proportion is available, how large should the sample be? |
Algebraic Expression:
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Hints: |
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Answer: 4148 (MUST ALWAYS ROUND UP FOR SAMPLE SIZE CALCULATIONS) |
6) Problem #PRAFJ6X "PRAFJ6X - ILL - Confidence intervals - proportions" |
A)
In a Gallop Poll of 1005 individuals, 452 thought they were worse off financially than a year ago. Find the 95% confidence interval for the true proportion of individuals that feel they are worse off financially. What is the lower limit of your confidence interval? Round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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7) Problem #PRAFJ5E "PRAFJ5E - Confidence intervals - proportions" |
A)
A survey of 90 families showed that 40 owned 2 or more cars. Find the 95% confidence interval of the true proportion of families who own 2 or more cars. What is the lower limit of your confidence interval? Round answer to the nearest hundredth. Link to t-table © STATS4STEM.ORG |
Algebraic Expression:
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B)
What is the upper limit of your confidence interval? Round answer to the nearest hundredth. |
Algebraic Expression:
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8) Problem #PRAFJTS "PRAFJTS - ILL - Confidence intervals - proportions" |
A)
A study by the University of Michigan found that one in five 13 and 14-year-olds is a sometime smoker. To see how the smoking rate of the students at a large school district compared to the national rate, the superintendent randomly surveyed two hundred 13 and 14-year-old students and found that 23% said they sometime smokers. Find the 99% confidence interval of the true proportion. What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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9) Problem #PRAFJTF "PRAFJTF - ILL - Confidence intervals - proportions" |
A)
A survey found that out of 200 workers, 168 said they were interrupted three or more times an hour by phone messages, faxes, etc. Find the 90% confidence interval of the population proportion of workers who are interrupted three or more times an hour. What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
Type .80 |
B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
Type .88 |
10) Problem #PRAFJMU "PRAFJMU - ILL - Proportion - CI's" |
A)
The proportion of students in private schools is around 11%. A random sample of 450 students from a wide geographic area indicated 55 attended private schools. Estimate the true proportion of students attending private schools with a 95% confidence. What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
Type .09 |
B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
Type .15 |
11) Problem #PRAJBDY "PRAJBDY - 239403 - An electronic chi..." |
A)
An electronic chip manufacturing company is hired by ACME Electronics Inc. to manufacture a complicated electronic chip for them. The manufacturing company charges a very high fee for each chip as they claim that the manufacturing process produces a high number of defects. In fact, the chip manufacturer claims that due to the unique chip design, 40 percent of the chips produced are defective. ACME is concerned that this may not be true. If the percentage defects are too high, then the company may be unreliable. If the percentage defects are too low, they may be paying too much for the chips as the company claims that the high defect rate is the reason for the high cost of the chip. They decide on a surprise inspection of the manufacturing company to test the manufacturing company's claim. Which is the correct hypothesis? A) Ho: p = .40 HA: p < .40 B) Ho: p-hat = .40 HA: p-hat ≠ .40 C) Ho: μ = .40 HA: μ ≠ .40 D) Ho: p=.40 HA: p≠.40 E) Ho: p-hat = .40 HA: p-hat < .40 © STATS4STEM.ORG |
Multiple Choice:
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B)
Which equation should be used to calculate the test statistic? A) B) C) D) E) |
Multiple Choice:
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C)
What conditions need to be checked? |
Check All That Apply:
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Hints: |
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D)
They take a simple random sample of 165 chips, of which 58 where found to be defective. Calculate the p-value. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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z = -1.271 |
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E)
If ACME wishes to use a significance level of 0.1, state the conclusion below: |
Ungraded Open Response: |
Hints: |
I calculated a p-value of 0.20, which is greater than the stated significance level of 0.1. Therefore, I fail to reject the null hypothesis. The data fails to support the claim that the proportion of defects produced by the chip manufacturer is different than 0.40. |
12) Problem #PRAJQ5V "PRAJQ5V - 251645 - Which equation is..." |
Which equation is used to calculate confidence intervals for proportions? A. B. C. D. © STATS4STEM.ORG |
Multiple Choice:
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13) Problem #PRAJTCR "PRAJTCR - 253780 - The following for..." |
A)
The following formulas come from the AP formula sheet. Which of the following formulas can be used to help one remember/create the the confidence interval formula for a problem pertaining to the difference of proportions? © STATS4STEM.ORG |
Multiple Choice:
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B)
Which of the formulas can be used to help one remember/create the test statistic needed for a hypothesis test for a problem pertaining to the difference of proportions? |
Multiple Choice:
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14) Problem #PRAJ7GW "PRAJ7GW - 265441 - Confidence Intervals - Proportions - Sample Size" |
How large a sample should be surveyed to estimate the true proportion of men who wear ear rings within 4% with 99% confidence? © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
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m = .04 z* = 2.576 |
Answer: 1037 (MUST ROUND UP) |
15) Problem #PRAJ7GX "PRAJ7GX - 265442 - 157568 - Confidence intervals - proportions - sample size" |
A)
A researcher wishes to estimate the proportion of squirrels that can be classified as red squirrels in a national park. She wants to construct a 90% confident interval that has a margin of error of 5%. a) How large a sample should be taken if it is estimated that 10% of all squirrels are red squirrels in the national park? © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
z* = 1.645 m = .05 |
Answer: 98 (MUST ROUND UP) |
B)
b) If no estimate is available for the proportion of red squirrels in the national park, how large should the sample be? |
Algebraic Expression:
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Hints: |
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z* = 1.645 m=0.05 n = 270.6025 Answer: 271 (MUST ROUND UP) |
16) Problem #PRAJ7GY "PRAJ7GY - 265443 - Confidence intervals - proportions" |
A)
In a Poll of 1123 chimpanzees, 612 thought they were being fed less berries than a year ago. Find the 99% confidence interval for the true proportion of chimps that feel like they are being fed less berries. What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
m = (z*)sqrt((p-hat)(1-p-hat)/n) |
z* = 2.576 n = 1123 |
m=0.038 |
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B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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m = .038 |
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17) Problem #PRAJ7GZ "PRAJ7GZ - 265444 - A manufacturing c..." |
A)
A manufacturing company is hired by Ford to manufcature a new eco friendly motor. The manufacturing company claims that the manufacturing process produces a high number of defects. In fact, they claim that that 35 percent of the motors produced are defective. Ford is concerned that this may not be true. If the percentage defects are too high, then the company may be unreliable. If the percentage defects are too low, they may be paying too much for the motors as the company claims that the high defect rate is the reason for the high cost of the motor. They decide on a surprise inspection of the manufacturing company to test the manufacturing company's claim. Which is the correct hypothesis? A) Ho: p = ..35 HA: p < .35 B) Ho: p-hat = .35 HA: p-hat ≠ .35 C) Ho: μ = .35 HA: μ ≠ .35 D) Ho: p=.35 HA: p≠.35 © STATS4STEM.ORG |
Multiple Choice:
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B)
They take a simple random sample of 160 motors, of which 49 where found to be defective. Test the following hypothesis at the .01 significance level. Ho: p=.35 HA: p≠.35 What is your final p-value for this problem? Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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C)
Reject or Fail to Reject? |
Multiple Choice:
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Hints: |
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18) Problem #PRAJ7G2 "PRAJ7G2 - 265445 - Which equation is..." |
Which equation is used to calculate confidence intervals for proportions? A. B. C. D. © STATS4STEM.ORG |
Multiple Choice:
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19) Problem #PRAJ7G3 "PRAJ7G3 - 265446 - Confidence intervals - proportions" |
A)
A survey of 110 families showed that 55 owned at least one pet. Find the 95% confidence interval of the true proportion of families who own at least one pet. What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
m = (z*)sqrt((p-hat)(1-p-hat)/n) |
z* = 1.960 n = 110 |
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Answer: .41 (ROUNDED) |
B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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m = .093 |
Answer: .59 or .6 |
20) Problem #PRAJ7G4 "PRAJ7G4 - 265447 - Confidence intervals - proportions" |
A)
A study by the Harvard University found that one in three 16 and 17-year-olds knows how to drive. To see how the driving rate of the students at a large school district compared to the national rate, the superintendent surveyed two hundred 16 and 17-year-old students and found that 39% said they know how to drive. Find the 99% confidence interval of the true proportion. What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. Link to t-table. © STATS4STEM.ORG |
Algebraic Expression:
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Hints: |
z* = 2.576 n = 200 |
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Answer = 0.30 (ROUNDED) |
B)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
m = .0888 |
Answer: .48 (ROUNDED) |
C)
Interpret your confidence interval in the context of the problem. |
Ungraded Open Response: |
21) Problem #PRAJ7G5 "PRAJ7G5 - 265448 - Confidence intervals - proportions" |
A)
In a small US city, it was believed that 85% of the voting public supported an increase in green space within the city. A survey of 200 random voters from the city was conducted. Of the voters questioned, 154 said they supported an increase in green space. Construct a 90% confidence interval of the proportion of voters who support an increase in green space within the city. What are the conditions that need to be checked before constructing a confidence interval? Check all that apply. © STATS4STEM.ORG |
Check All That Apply:
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Hints: |
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B)
To construct a confidence interval for this problem, which is the correct formula to use? A) B) C) D) E) |
Multiple Choice:
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C)
What is the lower limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
z* = 1.645 n = 200 |
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Answer: .72 (ROUNDED) |
D)
What is the upper limit of your confidence interval? Answer as a decimal, and round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
m = .0489 |
Answer: .82 (ROUNDED) |
E)
True or False: The following sentence would be considered a correct interpretation of the confidence interval: Based on the sample, we are 90 percent confident that the proportion of voters who support an increase in green space within the city is between 0.72 and 0.82. |
Multiple Choice:
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F)
A proper conclusion regarding the belief that 85% of the voting public supported an increase in green space within the city. |
Multiple Choice:
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22) Problem #PRAKKG7 "PRAKKG7 - 276982 - For problems that..." |
For problems that pertain to proportions one can say: © STATS4STEM.ORG |
Multiple Choice:
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23) Problem #PRAKMJR "PRAKMJR - Copier vs copier analysis" |
A)
A purchasing manager for a local school district was approached by a salesman for ACME copying machines. The salesman claimed "If we install a new machine, it will be the most reliable copier you've ever used!". The purchasing manager was intrigued as there was nothing more annoying than paper jams. However, he had fallen victim to past claims that had turned out to be untrue. He asked the salesman to prove his claim. The manager informed him that his current machine, a JAMFREE, is the most reliable copier that he has ever used and that the new machine must prove it's superiority. They decide to run an experiment. The experiment consisted of running 300 equally demanding batches through both machines. Some of the batches demanded staples, some double sided, but both machines were subject to the same tests. A week went by and the results came back. The new ACME machine produced 43 batches where at least 1 paper jam was reported out of a total of 300 batches run, while the JAMFREE produced 54 batches where at least 1 paper jam was reported out of a total of 300 batches run. What is the best formula to calculate the test statistic for this problem? A. B. C. D. E. F. © STATS4STEM.ORG |
Multiple Choice:
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B)
Which of the following represent the correct null and alternative hypothesis? Notation: A - ACME; J - JAMFREE
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Multiple Choice:
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C)
What assumptions and condition must be checked before proceeding with your test of significance? |
Check All That Apply:
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Hints: |
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D)
Calculate p-hat (not p-hat1 or p-hat2) for the formula shown below as it pertains to this problem. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
p-hatJAMFREE= 54/300 |
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E)
Based on the alternative hypothesis stated above, which of the following statements is correct? A) p-hat1 should be 54/300 and p-hat2 should be 43/300 so that the numerator of the fraction will be positive, and the z value will be positive too. This is ideal as the alternative hypothesis rejects on the right tail. B) p-hat1 should be 43/300 and p-hat2 should be 54/300 so that the numerator of the fraction will be negative, and the z value will be negative too. This is ideal as the alternative hypothesis rejects on the left tail. C) p-hat1 should be 54/300 and p-hat2 should be 43/300 so that the numerator of the fraction will be positive, and the z value will be positive too. This is ideal as the alternative hypothesis rejects on the left tail. D) p-hat1 should be 43/300 and p-hat2 should be 54/300 so that the numerator of the fraction will be negative, and the z value will be negative too. This is ideal as the alternative hypothesis rejects on the right tail. |
Multiple Choice:
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F)
Calculate the p-value for this problem. Round answer to the nearest hundredth. Link to z-table. |
Algebraic Expression:
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Hints: |
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G)
Which of the formulas found on the AP formula sheet can be used to help one remember/create the test statistic formula needed for a hypothesis test for a problem pertaining to the difference of proportions? |
Multiple Choice:
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H)
Using a significance level is 0.05, the best conclusion would be: A) I calculated a p-value of 0.11, which is greater than the stated significance level of 0.05. Therefore, we can reject the null hypothesis. B) Reject the null hypothesis. C) I calculated a p-value of 0.11, which is greater than the stated significance level of 0.05. Therefore, we fail to reject the null hypothesis. The data proves that the proportion of batches creating at least 1 paper jam is equal for ACME and JAMFREE copying machines. D) I calculated a p-value of 0.11, which is greater than the stated significance level of 0.05. Therefore, we reject the null hypothesis. The data supports the claim tthat the proportion of batches creating at least 1 paper jam is less for the ACME copying machine than the JAMFREE copying machine. E) I calculated a p-value of 0.11, which is greater than the stated significance level of 0.05. Therefore, we fail to reject the null hypothesis. F) I calculated a p-value of 0.11, which is greater than the stated significance level of 0.05. Therefore, we fail to reject the null hypothesis. The data fails to support the claim that the proportion of batches creating at least 1 paper jam is less for the ACME copying machine than the JAMFREE copying machine. G) Fail to reject the null hypothesis. |
Multiple Choice:
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24) Problem #PRAQU3D "PRAQU3D - Problem #402623" |
A)
A large college claims that the proportion of small classes, those classes with less than 20 students, is 53 percent. The student run college paper believes that this is incorrect, and that the proportion of classes having less than 20 students is actually less than 53 percent. To prove their claim, a group of student journalists randomly sample 51 classes. From this random sample, 23 were found to have less than 20 students. Which of following best defines the null and alternative hypothesis?
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Multiple Choice:
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B)
For this hypothesis test, what conditions need to be checked? |
Check All That Apply:
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C)
For this specific problem, refer to the formula below and determine the value of the statistic (not the test statistic). Round answer to the nearest hundredth. |
Algebraic Expression:
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D)
Refer to the formula above, determine the value of the parameter. Round answer to the nearest hundredth. |
Algebraic Expression:
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E)
Refer to the formula above, calculate the "standard deviation of statistic". Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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F)
Refer to the formula above, calculate the test statistic. Round answer to the nearest hundredth. |
Algebraic Expression:
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G)
Calculate the p-value for this hypothesis test. Round answer to the nearest hundredth. Link to z-table |
Algebraic Expression:
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Hints: |
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H)
If α = 0.1, which of the following would be the best conclusion? A) I calculated a p-value of 0.13, which is greater than the stated significance level of 0.1. Therefore, I fail to reject the null hypothesis. The data fails to support the claim that the proprtion of classes with less than 20 students is less than 53 percent. B) I calculated a p-value of 0.13, which is greater than the stated significance level of 0.1. Therefore, I reject the null hypothesis. The data proves the claim that the proprtion of classes with less than 20 students is 53 percent. C) I calculated a p-value of 0.13, which is greater than the stated significance level of 0.1. Therefore, I fail to reject the null hypothesis. The data supports the claim that the proprtion of classes with less than 20 students is 53 percent. D) I calculated a p-value of 0.13, which is greater than the stated significance level of 0.1. Therefore, I reject the null hypothesis. The data fails to support the claim that the proprtion of classes with less than 20 students is less than 53 percent. E) Fail to reject the null hypothesis. F) Reject the null hypothesis. |
Multiple Choice:
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25) Problem #PRAQU3E "PRAQU3E - Problem #402623" |
A)
A large social media site claims that 23 percent of registered users access their service on a daily basis. A group of skeptical investors believe that this claim is an exaggeration and that daily usage by registered users is less than 23 percent. To prove their claim, the investors randomly sample 50 registered users. From this random sample, 9 were found to use the site on a daily basis. Which of following best defines the null and alternative hypothesis?
© STATS4STEM.ORG |
Multiple Choice:
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B)
For this hypothesis test, which test statistic formula is most appropriate?
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Multiple Choice:
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C)
For this hypothesis test, what conditions need to be checked? |
Check All That Apply:
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D)
Calculate the test statistic. Round answer to the nearest hundredth. |
Algebraic Expression:
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Hints: |
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Therefore, z=-0.83 (ROUNDED) |
E)
Calculate the p-value for this hypothesis test. Round answer to the nearest hundredth. Link to z-table |
Algebraic Expression:
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Hints: |
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F)
Assuming α = 0.1, state your conclusion to the hypothesis test: |
Ungraded Open Response: |