A real estate conglomerate is analyzing the household size in a region for the purpose of developing a piece of land. Based on a land management’s report, several years ago the region had an average household size of 3.14 persons with the population standard deviation of 0.82 people. The developer is suspecting the average household size to be different now. A sociologist wishes to test it at a 5% level of significance with the information collected from a random sample of 75 households.

a. State the appropriate null and alternative hypothesis for the developer.

b. Compute the power of the hypothesis test to reject the null hypothesis if the true average household size in the region is 3.2 people.