Part a)

Calculate the statistic, set up the rejection region, interpret the result, and draw the sampling distribution.

i) H0: =10

H1: 10

Given that: =10, n=100, mean of X=10,=0.05.

ii)H0: =50

H1: <50

Given that: =15, n=100, mean of X =48, =0.05.

Part b)

A statistics practitioner is in the process of testing to determine whether 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 the mean of X =175 and s=22. Calculate the value of the test statistic of the test required to determine whether there is enough evidence to infer at the 5% significance level that the population mean is different from 180.