696 CHAPTER 13 Nonparametric Tests 3. t Test The bag of Hershey’s Kisses includes 75 of the candies. According to the label, the total weight is 340 g, so the candies should have a mean weight of 340>75 = 4.5333g. Use the sample of weights listed above to test the claim that they are from a population with a mean of 4.5333 g. Use a 0.05 significance level with a t test. What does the conclusion suggest about the claim of 340 g printed on the label? 4. Sign Test Repeat Exercise 3 using the sign test to test the claim that the sample of weights is from a population with a median of 4.5333 g. 5. Wilcoxon Signed-Ranks Test Repeat Exercise 3 using the Wilcoxon signed-ranks test to test the claim that the sample of weights is from a population with a median of 4.5333 g. 6.Confidence Interval Use the sample of Hershey’s Kisses weights on the previous page to construct a 95% confidence interval estimate of the population mean μ. What does the confidence interval suggest about the claim that Hershey’s Kisses have a mean weight of 4.5333 g? 7.Bootstrap Resampling Use the bootstrap resampling method with the sample of Hershey’s Kisses weights to construct a 95% confidence interval estimate of the population mean μ. What does the confidence interval suggest about the claim that Hershey’s Kisses have a mean weight of 4.5333 g? 8. Randomness Refer to the following ages at inauguration of the elected presidents of the United States (from Data Set 22 “Presidents” in Appendix B). Test for randomness above and below the mean. Do the results suggest an upward trend or a downward trend? 57 61 57 57 58 57 61 54 68 49 64 48 65 52 46 54 49 47 55 54 42 51 56 55 51 54 51 60 62 43 55 56 52 69 64 46 54 47 70 9.Sample Size Advances in technology are dramatically affecting different aspects of our lives. For example, the number of daily print newspapers is decreasing because of easy access to Internet and television news. To help address such issues, we want to estimate the percentage of adults in the United States who use a computer at least once each day. Find the sample size needed to estimate that percentage. Assume that we want 95% confidence that the sample percentage is within two percentage points of the true population percentage. 10. Cell Phones and Crashes: Analyzing Newspaper Report In an article from the Associated Press, it was reported that researchers “randomly selected 100 New York motorists who had been in an accident and 100 who had not been in an accident. Of those in accidents, 13.7 percent owned a cellular phone, while just 10.6 percent of the accident-free drivers had a phone in the car.” What is wrong with these results? Technology Project Past attempts to identify or contact extraterrestrial intelligent life have involved efforts to send radio messages carrying information about us earthlings. Dr. Frank Drake of Cornell University developed such a radio message that could be transmitted as a series of pulses and gaps. The pulses and gaps can be considered to be 1s and 0s. Listed on the next page is a message consisting of 77 entries of 0s and 1s. If we factor 77 into the prime numbers of 7 and 11 and then make an 11 * 7 grid and put a dot at those positions corresponding to a pulse of 1, we can get a simple picture of something. Assume that the sequence of 77 entries of 1s and 0s is sent as a radio message that is intercepted by extraterrestrial life with enough intelligence to have studied this book. If the radio message is tested using the methods of this chapter, will the
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