Chapter7 Test B

Name: ______Date: ______

1. / A quality control expert wants to estimate the proportion of defective components that are being manufactured by his company to within 2.5%. A sample of 300 components showed that 20 were defective. How large a sample is needed to estimate the true proportion of defective components with 99% confidence?
2. / A sample of 400 racing cars showed that 80 cars cost over $700,000. What is the 99% confidence interval of the true proportion of cars costing over $700,000?
3. / A 90% confidence interval around the variance was calculated. For , the confidence interval was 35.0–88.4. Give the variance of the sample.
4. / The average number of miles that 90 truckers drove in a day was 540 with a standard deviation of 40 miles. What is the 99% confidence interval of the true mean number of miles driven by all truckers?
5. / Which value of was used in the figure below?
6. / 8 squirrels were found to have an average weight of 9.5 ounces with a sample standard deviation is 0.20. Find the 95% confidence interval of the true mean weight.
7. / A researcher conducted a study of the access speed of 30 hard drives and concluded that his maximum error of estimate was 30. If he were to conduct a second study to reduce the maximum error of estimate to 6, about how many hard drives should he include in his new sample?
8. / A study of 70 professors showed that the time they spent on the average in creating test questions was 17.0 minutes per question. The standard deviation of the population is 3. Which of the following is the 90% confidence interval for the average number of minutes it takes to create a test question?
9. / In a study of 100 new cars, 27 of them were white. Find and where is the proportion of new cars that is white.
10. / A report states that 44% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 4% with 92% confidence?
11. / A college believes that 26% of applicants to that school have parents who have remarried. How large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 3% with 90% confidence?
12. / In a sample of 60 mice, a biologist found that 46% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run that maze in 30 seconds or less.
13. / In a study of size 16 where the variance is unknown, the distribution that should be used to calculate confidence intervals is what?
14. / A study of 60 bolts of carpet showed that their average length was 150 yards. The standard deviation of the population is 10 yards. Which of the following is the 99% confidence interval for the mean length per bolt of carpet?
15. / Using Table G, find the values for and for = .05 and n = 12.
16. / If is equal to 0.77, then is equal to what?
17. / A random sample of 100 voters found that 44% were going to vote for a certain candidate. Find the 90% limit for the population proportion of voters who will vote for that candidate.
18. / A report states that 42% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 6% with 95% confidence?
19. / A previous analysis of paper boxes showed that the the standard deviation of their lengths is 15 millimeters. A pakcer wishes to find the 98% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 4 millimeters?
20. / The winning team's scores in 13 high school basketball games were recorded. If the sample mean is 10.2 points and the sample standard deviation is 0.30 points, find the 98% confidence interval of the true mean.


Answer Key

1. / 661
2.
3. / 52.3
4.
5. / 1.65
6. / (9.27, 9.73)
7. / 750
8. / (16.41, 17.59)
9. / =0.27, =0.73
10. / 472
11. / 579
12. / 35.4% < p < 56.6%
13. / a t distribution with 15 degrees of freedom
14. / (146.67, 153.33)
15. / 4.575 and 19.675
16. / 0.23
17. / 35.8% < p < 52.2%
18. / 260
19. / 77
20. / (9.98, 10.42)

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