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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Using Correct Distribution. In Exercises 5โ8, assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) Find the critical value ,(b) find the critical value ,or (c) state that neither the normal distribution nor the t distribution applies.
Birth Weights Here are summary statistics for randomly selected weights of newborn girls: (based on Data Set 4 โBirthsโ in Appendix B). The confidence level is 95%.
In Exercises 9โ16, assume that each sample is a simplerandom sample obtained from a population with a normal distribution.
Insomnia Treatment A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. After treatment with zopiclone, 16 subjects had a mean wake time of 98.9 min and a standard deviation of 42.3 min (based on data from โCognitive Behavioral Therapy vs Zopiclone for Treatment of Chronic Primary Insomnia in Older Adults,โ by Sivertsen et al.,Journal of the American Medical Association,Vol. 295, No. 24). Assume that the 16 sample values appear to be from a normally distributed population and construct a 98% confidence interval estimate of the standard deviation of the wake timesfor a population with zopiclone treatments. Does the result indicate whether the treatment is effective?
Question:In Exercises 5โ8, use the given information to find the number of degrees of freedom, the critical values X2 L and X2R, and the confidence interval estimate of . The samples are from Appendix B and it is reasonable to assume that a simple random sample has been selected from a population with a normal distribution.
Heights of Men 99% confidence;n= 153,s= 7.10 cm.
Garlic for Reducing Cholesterol In a test of the effectiveness of garlic for lowering cholesterol, 49 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes (before minus after) in their levels of LDL cholesterol (in mg/dL) had a mean of 0.4 and a standard deviation of 21.0 (based on data from โEffect of Raw Garlic vs Commercial Garlic Supplements on Plasma Lipid Concentrations in Adults with Moderate Hypercholesterolemia,โ by Gardner et al., Archives of Internal Medicine, Vol. 167). Construct a 98% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL cholesterol?
Sample Size. In Exercises 29โ36, find the sample size required to estimate the population mean.
Mean Weight of Male Statistics Students Data Set 1 โBody Dataโ in Appendix B includes weights of 153 randomly selected adult males, and those weights have a standard deviation of 17.65 kg. Because it is reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males, let . How many male statistics students must be weighed in order to estimate the mean weight of all male statistics students? Assume that we want 90% confidence that the sample mean is within 1.5 kg of the population mean. Does it seem reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males?
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