5.23 Use the Central Limit Theorem applet again. Refer to the previous exercise. In the setting of Example 5.9, let’s approximate the sampling distribution for samples of size n = 2, 10, and 25 observations.
(a) For each sample size, compute the mean and standard deviation of .
(b) For each sample size, use the applet to approximate the sampling distribution. Report the estimated mean and standard deviation. Are they close to the true values calculated in part (a)?
(c) For each sample size, compare the shape of the sampling distribution with the Normal curve based on the central limit theorem.
(d) For this population distribution, what sample size do you think is needed to make you feel comfortable using the central limit theorem to approximate the sampling distribution of ? Explain your answer.