a. To test the following hypotheses, a statistics practitioner randomly sampled 100 observations and found x̄ = 106 and s = 35. Calculate the test statistic (and for Excel users, the p-value) of a test to determine whether there is enough evidence at the 1% significance level to infer that the alternative hypothesis is true.

H0: µ = 100

H1: µ > 100

b. Repeat part (a) with s = 25.

c. Repeat part (a) with s = 15.

d. Discuss what happens to the t-statistic when the standard deviation decreases.