45. Waist size revisited. A study commissioned by a clothing manufacturer measured the Waist Sizes of a random sample of 250 men. The mean and standard deviation of the Waist Sizes for all 250 men are 36.33 in and 4.019 inches, respectively. In Exercise 43 you looked at the histograms of simulations that drew samples of sizes 2, 5, 10, and 20 (with replacement).

The summary statistics for these simulations were as follows:

a) According to the Central Limit Theorem, what should the theoretical mean and standard deviation be for each of these sample sizes?

b) How close are the theoretical values to what was observed in the simulation?

c) Looking at the histograms in Exercise 43, at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?

d) What about the shape of the distribution of Waist Size explains your choice of sample size in part c?

Transcribed Image Text:

n mean st. dev. 2 36.314 2.855 5 36.314 1.805 10 36.341 1.276 20 36.339 0.895