Chapter 7: Q4 (page 347)
How Many? The examples in this section all involved no more than 20 bootstrap samples. How many should be used in real applications?
For a real application, at least 1000 samples should be used for bootstrapping to get more accuracy.
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Confidence Intervals. In Exercises 9โ24, construct the confidence interval estimate of the mean. Arsenic in Rice Listed below are amounts of arsenic (ฮผg, or micrograms, per serving) in samples of brown rice from California (based on data from the Food and Drug Administration). Use a 90% confidence level. The Food and Drug Administration also measured amounts of arsenic in samples of brown rice from Arkansas. Can the confidence interval be used to describe arsenic levels in Arkansas? 5.4 5.6 8.4 7.3 4.5 7.5 1.5 5.5 9.1 8.7
In Exercises 5โ8, use the relatively small number of given bootstrap samples to construct the confidence interval.Seating Choice In a 3M Privacy Filters poll, respondents were asked to identify their favourite seat when they fly, and the results include these responses: window, window, other, other. Letting โwindowโ = 1 and letting โotherโ = 0, here are ten bootstrap samples for those responses: {0, 0, 0, 0}, {0, 1, 0, 0}, {0, 1, 0, 1}, {0, 0, 1, 0}, {1, 1, 1, 0}, {0, 1, 1, 0}, {1, 0, 0, 1}, {0, 1, 1, 1}, {1, 0, 1, 0}, {1, 0, 0, 1}. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the proportion of respondents who indicated their favourite seat is โwindow.โ
Formats of Confidence Intervals.
In Exercises 9โ12, express the confidence interval using the indicated format. (The confidence intervals are based on the proportions of red, orange, yellow, and blue M&Ms in Data Set 27 โM&M Weightsโ in Appendix B.)
Orange M&Ms Express 0.179 < p < 0.321 in the form of .
Critical Thinking. In Exercises 17โ28, use the data and confidence level to construct a confidence interval estimate of p, then address the given question.
OxyContinThe drug OxyContin (oxycodone) is used to treat pain, but it is dangerous because it is addictive and can be lethal. In clinical trials, 227 subjects were treated with OxyContin and 52 of them developed nausea (based on data from Purdue Pharma L.P.).
a.Construct a 95% confidence interval estimate of the percentageof OxyContin users who develop nausea.
b.Compare the result from part (a) to this 95% confidence interval for 5 subjects who developed nausea among the 45 subjects given a placebo instead of OxyContin: 1.93% <p< 20.3%. What do you conclude?
Critical ValueFor the survey described in Exercise 1 โCelebrities and the Law,โ find the critical value that would be used for constructing a 99% confidence interval estimate of the population proportion.
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