1.14 (E Section 1.4.3)

In this simulation exercise we consider the quality of the asymptotic interval estimates discussed in Section 1.4.3. As data generating process we consider the t(3) distribution that has mean equal to zero and variance equal to three. We focus on the construction of interval estimates of the mean and on corresponding tests.

a. Generate a sample of n ¼ 10 independent drawings from the t(3) distribution. Let y be the sample mean and s the sample standard deviation.

Compute the interval y 2s=

ffiffiffinp . Reject the null hypothesis of zero mean if and only if this interval does not include zero.

b. Repeat the simulation run of a 10,000 times and compute the number of times that the null hypothesis of zero mean is rejected.

c. Repeat the simulation experiment of a and b for sample sizes n ¼ 100 and n ¼ 1000 instead of n ¼ 10.

d. Give an explanation for the simulated rejection frequencies of the null hypothesis for sample sizes n ¼ 10, n ¼ 100, and n ¼ 1000.