Take 30 slips of paper and label five each -4 and 4, four each -3 and 3 , three each -2 and 2 , and two each \(-1,0\) and 1 .

(a) If each slip of paper has the same probability of being drawn, find the probability of getting \(-4,-3,-2,-1,0,1,2,3,4\) and find the mean and the variance of this distribution.

(b) Draw 50 samples of size 10 from this population, each sample being drawn without replacement, and calculate their means.

(c) Calculate the mean and the variance of the 50 means obtained in part (b).

(d) Compare the results obtained in part

(c) with the corresponding values expected according to Theorem 6.1. That \(\mu\) and \(\sigma^{2}\) were obtained in part (a)

Data From Theorem 6.1

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Theorem 6.1 If a random sample of size n is taken from a population having the mean and the variance o, then X is a random variable whose distribution has the mean . For samples from infinite populations the variance of this distribution is For samples from a finite population of size N the variance is n 02 N-n n N-1'