364 CHAPTER 7 Estimating Parameters and Determining Sample Sizes a. Use the bootstrap method with 1000 bootstrap samples to find a 95% confidence interval estimate of s. b. Find the 95% confidence interval estimate of s found by using the methods of Section 7-3. c. Compare the results. If the two confidence intervals are different, which one is better? Why? 24.Analysis of Last Digits Repeat Exercise 23 “Analysis of Last Digits” using the mean instead of the standard deviation. Compare the confidence interval to the one that would be found using the methods of Section 7-2. 7-4 Beyond the Basics 25.Effect of the Number of Bootstrap Samples Repeat Exercise 23 “Analysis of Last Digits” using 10,000 bootstrap samples instead of 1000. What happens? 26.Distribution Shapes Use the sample data given in Exercise 23 “Analysis of Last Digits.” a. Do the original sample values appear to be from a normally distributed population? Explain. b. Do the 1000 bootstrap samples appear to have means that are from a normally distributed population? Explain. c. Do the 1000 bootstrap samples appear to have standard deviations that are from a normally distributed population? Explain. 27.Confirming the Requirement of Symmetry Use the sample data listed in Exercise 1 to generate 1000 bootstrap samples, then find the mean in each of those samples. Construct a histogram of the 1000 bootstrap sample means. Does it appear to be approximately symmetric as required? 28.Estimating the Median Use the sample data listed in Exercise 1 “Bootstrap Requirements” to generate 1000 bootstrap samples, and find the median in each of those samples. After obtaining the 1000 sample medians, find the 95% confidence interval estimate of the population median by evaluating P2.5 and P97.5 from the sorted 1000 medians. Given that the sample times in Exercise 1 are from the 50 times in Data Set 20 “Alcohol and Tobacco in Movies” and those 50 times have a median of 5.5, how well did the bootstrap method work to create a “good” confidence interval? 1. Female Motorcycle Owners Here is a 95% confidence interval estimate of the percentage of motorcycle owners who are female: 17.5% 6 p 6 20.6% (based on data from the Motorcycle Industry Council). What is the best point estimate of the percentage of motorcycle owners who are women? 2.Interpreting CI Write a brief statement that correctly interprets the confidence interval given in Exercise 1 “Female Motorcycle Owners.” 3.Critical Value For the survey described in Exercise 1 “Female Motorcycle Owners,” find the critical value that would be used for constructing a 99% confidence interval estimate of the population proportion. 4.Loose Change USA Today reported that 40% of people surveyed planned to use accumulated loose change for paying bills. The margin of error was given as {3.1 percentage points. Identify the confidence interval that corresponds to that information. 5. Sample Size for Proportion Find the sample size required to estimate the percentage of statistics students who take their statistics course online. Assume that we want 95% confidence that the proportion from the sample is within two percentage points of the true population percentage. 6.Sample Size for Mean Find the sample size required to estimate the mean IQ of airline pilots. Assume that we want 99% confidence that the mean from the sample is within two IQ points of the true population mean. Also assume that s = 15. Chapter Quick Quiz
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