21.41 A sampling distribution, continued. Exercise 21.39 presents 50 sample means x¯

from 50 random samples of size 100. Using a calculator, find the mean and standard error of these 50 values. Then answer these questions.

a. The mean of the population from which the 50 samples were drawn is μ=0.5 if the random number generator is accurate. What do you expect the mean of the distribution of x¯’s from all possible samples to be? Is the mean of these 50 samples close to this value?

b. The standard error of the distribution of x¯ from samples of size n=100 is supposed to be σ/10, where σ is the standard deviation of individuals in the population. Use this fact and the standard deviation you calculated for the 50 x¯’s to estimate σ.