21.41 A sampling distribution, continued. Exercise 21.39 presents 50 sample means 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 ’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 from samples of size n = 100 is supposed to be , where σ is the standard deviation of individuals in the population. Use this fact with the standard deviation you calculated for the 50 ’s to estimate σ.