AP Statistics: Inference for Quantitative Data (Means) Practice Test

1. Question

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500. Provide a 98% confidence interval for the true mean cost of repair.

11,000 ± 987.6
11,000 ± 1,456.6
11,000 ± 1,275.5
11,000 ± 1,366.7
11,000 ± 1,188.77

2. Question

Suppose you have a normally distributed variable with known variance. How many standard errors do you need to add and subtract from the sample mean so that you obtain 95% confidence intervals?

2.035
1.98
1.645
1.99
1.96

3. Question

The population standard deviation is 7. Our sample size is 36. What is the 95% margin of error for:
1) the population mean; 2) the sample mean

1) 14.567; 2) 4.445
1) 11; 2) 3
1) 15.554; 2) 3.656
1) 12.266; 2) 3.711
1) 13.720; 2) 2.287

4. Question

The 95% confidence interval created for the difference in means between two training programs for middle distance college runners is (−4.5, 6.5). The variable being measured is the improvement in seconds of mile times over the course of a season. One program has more speed work and intervals, while the other focuses more on distance training. What does the confidence interval tell us about the difference in the two programs?

The mean improvement of 1 second ((6.5−4.5)×0.5=1) is too small to matter, so reject the null. There is no evidence that one program is better at reducing miles times.
Zero is not in the interval, so reject the null. This is evidence that one program is significantly better at reducing mile times.
The confidence interval is large, so one program is clearly better at reducing mile times than the other.
6.5 is greater than |−4.5|, so reject the null. This is evidence that one program is better at reducing mile times than the other.
Zero is in the interval, so do not reject the null. There is no evidence that one program is better than the other.

5. Question

Suppose you conduct a paired z-test to assess whether two group means significantly differ and find a z-score of 1.645. At what alpha level would this cause you to reject the null?

0.20
0.10
0.05
0.01

6. Question

What is the standard deviation of each (and every) sample mean?

.7
.65
.35
.875
.9

7. Question

An exercise scientist wanted to test the effectiveness of a new program designed to increase the flexibility of senior citizens. They recruited participants and rated their flexibility according to a standard scale before starting the program. The participants all went through the program and had their flexibility rated again after a month. The scientist wants to test if the flexibility ratings are significantly higher after a month of the program. Assume that these participants can be considered a representative sample and that all other necessary conditions for inference were met. Which of these is the most appropriate test and alternative hypothesis?

8. Question

Owen lives in New York City and his brother Karson lives in Boston. They both complained about the high prices of avocado in their neighborhoods, so they decided to test whether there’s a difference in the average price of avocado. Each of them took a random sample of shops in their neighborhoods and got the price of avocado from each shop. Then, they calculated the average price in each group. Assume that all conditions for inference have been met. Which of these is the most appropriate test and alternative hypothesis?

9. Question

Jenny wants to compare the amount of weight people lose at her gym using two popular, non-overlapping weight-loss programs, Shred It and Burn It. She randomly samples people who use each program and tracks their weight loss. Here is a summary of the results:Jenny wants to use these results to carry out a two-sample t test to determine if the mean weight losses are significantly different for the two programs. Assume that all conditions have been met. Which of the following would be an appropriate test statistic for Jenny’s test?

10. Question

Researchers wanted to see if people who exercise regularly sleep better than people who don’t. They took a random sample of adult males and surveyed them about their exercise routine and their sleep duration. Here is a summary of the results:The researchers want to use these results to test H 0 : μ Exercise ‒ μ No exercise = 0 versus H a : μ Exercise ‒ μ No exercise > 0. Assume that all conditions have been met. Which of the following would be an appropriate test statistic for the researchers test?

11. Question

A media streaming service allows users to watch shows on their smartphones or tablets. An analyst wondered if users watching on tablets spend more time watching shows than users on smartphones. They took a separate random sample of each type of user to see how many hours they watched in total last month. Here is a summary of the results:The analyst wants to use these results to test H 0 : μ T ‒ μ S = 0 versus H a : μ T ‒ μ S > 0. Assume that all conditions have been met. What is the P-value associated with these sample results?

P-value < 0.01
0.01 ≤ P-value < 0.05
0.05 ≤ P-value < 0.10
0.10 ≤ P-value < 0.20
P-value ≥ 0.20

12. Question

A economist studying income in Norway and the United States wanted to compare the average annual income between the two countries. The economist obtained incomes for a random sample of people from each country and converted the incomes in the Norway sample to US dollars. Here is a summary of the annual incomes for the people in each sample (represented in thousands of US dollars): They want to use these results to test H 0 : μ N ‒ μ S = 0 versus H a : μ N ‒ μ S ≠ 0. Assume that all conditions have been met. What is the P-value associated with these sample results?

P-value < 0.01
0.01 ≤ P-value < 0.05
0.05 ≤ P-value < 0.10
0.10 ≤ P-value < 0.20
P-value ≥ 0.20

13. Question

Katie grows two varieties of pears—Bosc and Anjou. She took a sample of each variety to test if their mean weights were significantly different. Here is a summary of her results (weights are shown in grams): Katie wants to use these results to test H 0 : μ B = μ A versus H a : μ B ≠ μ A . Assume that all conditions for inference have been met. Based on the interval, what do we know about the corresponding P-value and conclusion at the α = 0.05 level of significance?

The P-value is less than α=0.05 and she should conclude that there is a difference between the means.
The P-value is less than α=0.05 and she cannot conclude that there is a difference between the means.
The P-value is greater than α=0.05 and she should conclude that there is a difference between the means.
The P-value is greater than α=0.05 and she cannot conclude that there is a difference between the means.

14. Question

An economist studying income in Argentina and Brazil wanted to compare the average annual income between the two countries. The economist obtained incomes for a random sample of people from each country to test if the average income in Argentina was higher. Here are the results of the test (incomes are shown in thousands of international dollars):At the α = 0.01 level of significance, is there sufficient evidence to conclude that the average income is higher in Argentina?

Yes, since the P-value is greater than 0.01.
Yes, since the test statistic is greater than 0.01.
No, since the P-value is greater than 0.01.
No, since the test statistic is greater than 0.01.

15. Question

The probability that she fails to reject the null hypothesis is 0.015%
The probability that she rejects the null is 0.015%
She can be 99.85% confident that the alternative hypothesis is true
About 0.15% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.
About 99.85% of all samples would product a test statistics at least as extreme as ours if the null hypothesis is true.

16. Question

When p-value is greater than alpha, we…

Accept H o
Fail to reject H o
Accept H a
Reject H o

17. Question

What does it mean when a test is statistically significant?

it has reached alpha level status
the test statistic had a P-value higher than the alpha level
the test statistic had a P-value lower than the alpha level
it is important in practical terms

18. Question

A guidance counselor wishes to determine the mean number of changes in academic major by college students to within ± 0.1 at a 90 percent confidence level. What sample size should be chosen if it is known that the standard deviation is 0.45?

8
54
55
78
110

19. Question

Given an experiment with H 0 : μ = 25; H a : μ > 25, and a possible true population value of 26, which of the following increase with an increase in the sample size n?

The probability of a Type I error
The probability of a Type II error
The power of the test
The significance level α

AP Statistics: Inference for Quantitative Data (Means) Practice Test

AP Statistics: Inference for Quantitative Data (Means) Practice Test

AP Statistics: Inference for Quantitative Data (Means) Practice Test

Quiz Summary

Information

Results

Results

Categories

1. Question

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500. Provide a 98% confidence interval for the true mean cost of repair.

2. Question

Suppose you have a normally distributed variable with known variance. How many standard errors do you need to add and subtract from the sample mean so that you obtain 95% confidence intervals?

3. Question

The population standard deviation is 7. Our sample size is 36. What is the 95% margin of error for:
1) the population mean; 2) the sample mean

4. Question

5. Question

Suppose you conduct a paired z-test to assess whether two group means significantly differ and find a z-score of 1.645. At what alpha level would this cause you to reject the null?

6. Question

What is the standard deviation of each (and every) sample mean?

7. Question

8. Question

9. Question

10. Question

11. Question

12. Question

13. Question

14. Question

15. Question

16. Question

When p-value is greater than alpha, we…

17. Question

What does it mean when a test is statistically significant?

18. Question

A guidance counselor wishes to determine the mean number of changes in academic major by college students to within ± 0.1 at a 90 percent confidence level. What sample size should be chosen if it is known that the standard deviation is 0.45?

19. Question

Given an experiment with H 0 : μ = 25; H a : μ > 25, and a possible true population value of 26, which of the following increase with an increase in the sample size n?

Average score
Your score

AP Statistics: Inference for Quantitative Data (Means) Practice Test

AP Statistics: Inference for Quantitative Data (Means) Practice Test

AP Statistics: Inference for Quantitative Data (Means) Practice Test

Quiz Summary

Information

Results

Results

Categories

1. Question

An automotive engineer wants to estimate the cost of repairing a car that experiences a 25 MPH head-on collision. He crashes 24 cars, and the average repair is $11,000. The standard deviation of the 24-car sample is $2,500. Provide a 98% confidence interval for the true mean cost of repair.

2. Question

Suppose you have a normally distributed variable with known variance. How many standard errors do you need to add and subtract from the sample mean so that you obtain 95% confidence intervals?

3. Question

The population standard deviation is 7. Our sample size is 36. What is the 95% margin of error for: 1) the population mean; 2) the sample mean

4. Question

5. Question

Suppose you conduct a paired z-test to assess whether two group means significantly differ and find a z-score of 1.645. At what alpha level would this cause you to reject the null?

6. Question

What is the standard deviation of each (and every) sample mean?

7. Question

8. Question

9. Question

10. Question

11. Question

12. Question

13. Question

14. Question

15. Question

16. Question

When p-value is greater than alpha, we…

17. Question

What does it mean when a test is statistically significant?

18. Question

A guidance counselor wishes to determine the mean number of changes in academic major by college students to within ± 0.1 at a 90 percent confidence level. What sample size should be chosen if it is known that the standard deviation is 0.45?

19. Question

Given an experiment with H 0 : μ = 25; H a : μ > 25, and a possible true population value of 26, which of the following increase with an increase in the sample size n?

The population standard deviation is 7. Our sample size is 36. What is the 95% margin of error for:
1) the population mean; 2) the sample mean