a. A statistics practitioner is in the process of testing to determine whether there is enough evidence to infer that the population mean is different from 180. She calculated the mean and standard deviation of a sample of 200 observations as x̄ = 175 and s = 22. Calculate the value of the test statistic of the test required to determine whether there is enough evidence at the 5% significance level.

b. Repeat part (a) with s = 45.

c. Repeat part (a) with s = 60.

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