On the computer, we draw 500 random samples of size 5 from the distribution of 1

Question

On the computer, we draw 500 random 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, we compute the sample mean x, the sample standard deviation s, and the test statistic t given by where n = 5 and mu_0 = 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 mu_0 is the population mean for ln(Alcoh_dr + 1).

Explanation / Answer

According to Central limit theorem, if repeated random sample sof size N are drwan from any population with mean mu and standard deviation sigma, then as N become slarge, sampling distribution of sample mean swil approach normality.Therefore, the t values should follow normal distribution [repated samples of size N=5 are drawn from a sample of 173 American nurses].

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