A Corporation is looking to invest in the health food industry. It is considering the creation of a health-drink franchise called Gray Juice. The investment department of the Mean Corporation want to investigate the feasibility of this venture by examining the profits of similar franchises. It believes that the venture will be feasible if an average annual profit of more than $81,000 can be expected from each Gray Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $7,900.
The Mean Corporation's statisticians would like to construct a hypothesis test for the population mean annual profit earned by health-drink franchises. A random sample of 50 franchises was chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $82,441.
The hypotheses that were used by the statisticians were
and the test statistic was found to be 1.29 (to 2 decimal places).
Calculate the p-value for this test, giving your answer as a decimal to 4 decimal places.
Part B: considering the situation posed above with the Corporation and interest in a health-drink franchise, given the p-value you calculated above and a 5% significance level, which of the following is an appropriate conclusion for the test carried out?
a. Reject the null hypothesis. b. Fail to reject the alternative hypothesis. c. Reject the alternative hypothesis. d. Fail to reject the null hypothesis.