B&C) Reject / not reject / accept The Mean Corporation would like to invest in t
ID: 3050690 • Letter: B
Question
B&C) Reject / not reject / accept The Mean Corporation would like to invest in the booming health food industry. It is considering the creation of a health-drink franchise called Goose Juice. The investment department of the Mean Corporation wants 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 $88,000 can be expected from each Goose Juice that is opened. It is known that the annual profits earned by health-drink franchises has a population standard deviation of $7,300. Mean Corporation The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit (H) earned by health-drink franchises. A random sample of 60 franchises were chosen and their annual profit for the previous financial year was recorded. The mean annual profit for the sample was calculated as $89,250. The hypotheses that will be used by the statisticians are Ho: = 88,000 and Ha : > 88,000. a) Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places. b) Using the test statistic for the Mean Corporation's hypothesis test and level a = 0.05, the Mean Corporation should the null hypothesis. c) If the sample size is increased to 130 (but the sample mean remains unchanged), the Mean Corporation should the null hypothesis.Explanation / Answer
n= 60
sample mean = 89250
population sd = 7300
mu = 88000
a. Z = (M - ) / (2 / n)
Z = (89250 - 88000) / (53290000 / 60)
Z = 1250 / 942.42595
Z = 1.32636
b. p value = 0.0924
p value > alpha
So , we fail to reject the null hypothesis.
c.
Z = (M - ) / (2 / n)
Z = (89250 - 88000) / (53290000 / 130)
Z = 1250 / 640.25235
Z = 1.95236
The z score is 1.95236. The p value is 0.02559.
p value < alpha
we reject the null hypothesis.
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