424 CHAPTER 8 Hypothesis Testing 11. Taxi Times Assume that Friday morning taxi-cab rides have times with a standard deviation of s = 9.9 minutes (based on Data Set 32 “Taxis” in Appendix B). A cab driver records times of rides during a Friday afternoon time period and obtains these statistics: n = 12, x = 19.3 minutes, s = 13.2 minutes. Use a 0.05 significance level to test the claim that these Friday afternoon times have greater variation than the Friday morning times. 12. Spoken Words Couples were recruited for a study of how many words people speak in a day. A random sample of 56 males resulted in a mean of 16,576 words and a standard deviation of 7871 words. Use a 0.01 significance level to test the claim that males have a standard deviation that is greater than the standard deviation of 7460 words for females (based on Data Set 14 “Word Counts”). 13. Aircraft Altimeters The Skytek Avionics company uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in the errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production method. If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action? -42 78 -22 -72 -45 15 17 51 -5 -53 -9 -109 14. Bank Lines The Jefferson Valley Bank once had a separate customer waiting line at each teller window, but it now has a single waiting line that feeds the teller windows as vacancies occur. The standard deviation of customer waiting times with the old multiple-line configuration was 1.8 min. Listed below is a simple random sample of waiting times (minutes) with the single waiting line. Use a 0.05 significance level to test the claim that with a single waiting line, the waiting times have a standard deviation less than 1.8 min. What improvement occurred when banks changed from multiple waiting lines to a single waiting line? 6.5 6.6 6.7 6.8 7.1 7.3 7.4 7.7 7.7 7.7 15. Weights of Peanut Butter Cups Listed below are weights (grams) of randomly selected Reese’s Peanut Butter Cup Miniatures. Use the listed sample data to test the claim that the sample is from a population having weights with a standard deviation equal to 0.2000 g. Use a significance level of a = 0.05. 8.639 8.689 8.548 8.980 8.936 9.042 16. Mint Specs Listed below are weights (grams) from a simple random sample of post-1983 pennies (from Data Set 40 “Coin Weights” in Appendix B). U.S. Mint specifications now require a standard deviation of 0.0230 g for weights of pennies. Use a 0.01 significance level to test the claim that pennies are manufactured so that their weights have a standard deviation equal to 0.0230 g. Does the Mint specification appear to be met? 2.5024 2.5298 2.4998 2.4823 2.5163 2.5222 2.4900 2.4907 2.5017 Large Data Sets from Appendix B. In Exercises 17 and 18, use the data set from Appendix B to test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. 17. Los Angeles Commute Time Use the 1000 Los Angeles commute times listed in Data Set 31 “Commute Times” to test the claim that the sample is from a population with a standard deviation equal to 20 minutes. Use a 0.01 significance level. Also determine whether the distribution of the 1000 Los Angeles commute times satisfies the requirements of this hypothesis test. 18. Height Based on the results of the 1988 survey of U.S. Army personnel, the standard deviation of heights of males is 66.8 mm. Use the heights (mm) of the 4082 males listed in Data Set 3 “ANSUR II 2012” in Appendix B to test the claim that this sample collected in 2012 is from a population with a standard deviation different from 66.8 mm. Use a 0.05 significance level. Also determine whether the distribution of the 4082 heights satisfies the requirements of this hypothesis test.
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