1) Problem #PRAE9UK "PRAE9UK - Sampling Proportions - copy of 147955" |
A)
In a given year, J and J Manufacturing produces 10,000 widgets, where 19% of the products are defective. Suppose the manufacturing engineers decide to sample 150 widgets. As a decimal, what is the mean of the sampling distribution of p-hat? © STATS4STEM.ORG |
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B)
Using Rweb and the code found below, create a histogram of the sampling distribution for p-hat. x=rbinom(10000, 150, .19) p.hat=x/150 hist(p.hat, breaks=15) # construct a normal probability plot qqnorm(p.hat) qqline(p.hat) Review the histogram and the normal probability plot to assess normality. Does the sampling distribution for p-hat appear to be normal? Hint: Here is a link to review normal probability plots. |
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C)
Review your histogram again. Use the following code if needed. x=rbinom(10000, 150, .19) p.hat=x/150 hist(p.hat, breaks=15) Using what you know about the density curve of the normal distribution, estimate the standard deviation through visual inspection of the histogram. |
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D)
Round answer to the nearest thousands (3 decimal places). What is the standard deviation of the sampling distribution of p-hat? In other words, calculate p-hat using the formula for standard deviation? Round answer to the nearest thousands (3 decimal places). |
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E)
Are the required conditions been met to use the normal approximation for p-hat? Hint: Make sure you remember these requirement and always use them before assuming normality. |
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F)
We can approximate the sampling distribution of p-hat with which distribution? |
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G)
What is the probability p-hat will be less than .15? Anwer as a decimal rounded to nearest hundredth. |
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Calculate z = (0.15 - 0.19)/0.032 |
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H)
What is the probability p-hat will fall between .14 and .20? Anwer as a decimal rounded to nearest hundredth. |
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I)
What is the probability p-hat will be greater than .20? Anwer as a decimal rounded to nearest hundredth. |
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J)
What is the probability p-hat will fall between .15 and .18? Anwer as a decimal rounded to nearest hundredth. |
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2) Problem #PRAJNPH "PRAJNPH - 249278 - A speed reading c..." |
A)
A speed reading company claims that their product reduces the time it takes to read a page. To prove their claim, 12 random individuals were timed on their ability to read a page. This data was recorded as sample A. The individuals then took a two-day speed reading class offered by the company and were timed again after taking the class. Their second recorded time was recorded as sample B. To prove their claim, which of the following test statistics should be used? A. B. C. D. E. © STATS4STEM.ORG |
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B)
Calculate the test statistic, t. Round answer to the nearest hundredth. |
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s = 4.843 μ0 = 0 |
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C)
Calculate the p-value for this hypothesis test. Round answer to the nearest hundredth. |
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To calculate the p-value using a TI-83, you would use the following procedure: Click 2nd -> DISTR -> tcd(-10, -1.43, 11) ### tcd( LOWER #, HIGHER #, df) -> Use 10 and -10 for higher and lower limits R/Rweb Instructions: To calculate the p-value using R/Rweb, you would use the following function: pt(-1.43, 11) ### P(X<t) = pt(t, df) |
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D)
Calculate the margin of error for a 99% confidence interval. Round answer to the nearest hundredth. |
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3) Problem #PRAJNDM "PRAJNDM - STATS4STEM.ORG" |
A)
Twenty-one elastic bands were randomly divided into two groups. One of the sets was placed in hot water (60-65 degrees C) for four minutes, while the other was left at ambient temperature. After a wait of about ten minutes, the amounts of stretch, under a 1.35 kg weight, were recorded. A researcher wishes to prove that heated bands stretch more than bands stretched while at ambient temperature.What is the best formula to calculate the test statistic for this problem? A. B. C. D. E. © STATS4STEM.ORG |
Multiple Choice:
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B)
Which of the following represent the correct null and alternative hypothesis? Notation: H - Heated; A - Ambient A) H0: μH = 0 Ha: μH < μA B) H0: μH = μA Ha: μH < μA C) H0: μH = 0 Ha: μH ≠ μA D) H0: μH = μA Ha: μH > μA E) H0: μH ≠ μA Ha: μH > μA F) H0: μH = 0 Ha: μH > μA G) None of the above |
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C)
What assumptions and condition must be checked before proceeding with your test of significance? |
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D)
Calculate the test statistic, t, for this problem. Round answer to the nearest hundredths. |
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Also, make sure to calculate t using an x-bar and s rounded to at least the thousands place. If you round x-bar and s to the hundredths place, your t value may be off by too much. ROUNDING EXAMPLE : x-bar = 3.215 (GOOD) x-bar = 3.22 (BAD) |
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E)
What is the degrees of freedom for this problem? If using technology, round answer to the nearest hundredth. |
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If using technology, df = 18.9158 or 18. 92 (More accurate) *** Both answers are acceptable, based on which method you choose to use. |
F)
Using either the TI-83 or R/Rweb, calculate the p-value. Round answer to the nearest hundredth. |
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To calculate the p-value using a TI-83, you would use the following procedure: Click 2nd -> DISTR -> tcd(1.99, 10, 9) ### tcd( LOWER #, HIGHER #, df) -> Use 10 and -10 for higher and lower limits R/Rweb Instructions: To calculate the p-value using R/Rweb, you would use the following function: 1 - pt(1.99, 9) ### P(X<t) = pt(t, df) |
p-value = 0.04 (Conservative Estimate) If using technology, df = 18.9158 p-value = 0.03 (More accurate) |
G)
Please state your conclusion for this hypothesis test in the context of the problem. |
Ungraded Open Response: |
H)
For this problem, calculate the margin of error for a 99% confidence interval. Round answer to the nearest hundredth. |
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margin of error = 15.37 (Conservative Estimate) If using technology, df = 18.9158 margin of error = 13.54 (More accurate) *** Both answers are acceptable depending on approach. |
4) Problem #PRAJB49 "PRAJB49 - 240094 - The mean SAT..." |
A)
The SAT scores for students from Boston Latin School are normally distributed with a mean of 1910 with a standard deviation is 450. Ten random students were asked to report their SAT score to their AP Statistics teacher, Mr. Simoneau. What is the probability that the mean of their score will be 2200 or higher? Round answer to the nearest hundredth. Link to z-table. © STATS4STEM.ORG |
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B)
What is the probability that 1 randomly chosen student will have a score of 2200 or higher? Round answer to the nearest hundredth. |
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5) Problem #PRAJBY6 "PRAJBY6 - 239967 - Helga plays a gam..." |
Helga plays a game where she wins on average once every 8 games. Let X be the number of games she must play until she wins. What is the standard deviation of X? Round answer to the nearest hundredths. © STATS4STEM.ORG |
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6) Problem #PRAJBPP "PRAJBPP - 239673 - The test scores f..." |
The test scores for an AP Statistics class have the distribution N(85, 5). How high would a student need to score to be in the top twenty percent? Link to z-table. *** Round answer to the nearest whole number. *** © STATS4STEM.ORG |
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Answer = 89 (ROUNDED) |
7) Problem #PRAJH4V "PRAJH4V - 245848 - Dana is an 83% fr..." |
Dana is an 83% free-throw shooter. What is the probability that his first success is on the third try? Round answer to the nearest hundredth. © STATS4STEM.ORG |
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The equation is: P(x=n) = qn-1 x p Where q = .17, n = 3, and p = .83 |
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