Chapter 6, Problem 81P

On the computer, draw 1000 bootstrap samples of size 5 from the distribution of 173 values of ln(alcohol DR [diet record] + 1) in the Data Set VALID.DAT, where alcoh_dr is the amount of alcohol consumed as reported by diet record by a group of 173 American nurses who recorded each food eaten on a real-time basis, over four 1-week periods spaced approximately 3 months apart over the course of 1 year. For each sample of size 5, compute the sample mean $\bar{x}$, the sample standard deviation s, and the test statistic t given by

$t=\frac{\bar{x}-{\mu }_0}{s/\sqrt{n}}$

where n = 5 and μ₀ = overall mean of ln(alcohol DR + 1)

over the 173 nurses = 1.7973.

What distribution should the t-values follow if the central-limit theorem holds? Assume μ₀ is the population mean for ln(alcoh_dr + 1).