The Mean Corporation would like to invest in the booming healthfood industry. It is considering the creation of a health-drinkfranchise called Goose Juice. The investment department of the MeanCorporation wants to investigate the feasibility of this venture byexamining the profits of similar franchises. It believes that theventure will be feasible if an average annual profit of more than$89,000 can be expected from each Goose Juice that is opened. It isknown that the annual profits earned by health-drink franchises hasa population standard deviation of $8,200.
The Mean Corporation's statisticians would like to construct ahypothesis test for the mean annual profit (μ) earned byhealth-drink franchises. A random sample of 70 franchises werechosen and their annual profit for the previous financial year wasrecorded. The mean annual profit for the sample was calculated as$90,250. The hypotheses that will be used by the statisticians areH0: μ = 89,000 and Ha: μ > 89,000.
A.) Calculate the test statistic (z) that corresponds to thesample and hypotheses. Give your answer to 3 decimal places.
Z =
B.) Using the test statistic for the Mean Corporation'shypothesis test and level α = 0.05, the Mean Corporation should(accept, reject, not reject) the null hypthesis.
C.) If the sample size is increased to 170 (but the sample meanremains unchanged), the Mean Corporation should (accept, reject,not reject) the null hypothesis.
