The Mean Corporation would like to invest in the booming health food industry. I

Question

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 profit earned by health-drink franchises has a population standard deviation of $8, 600. The Mean Corporation's statisticians would like to construct a hypothesis test for the mean annual profit (mu) earned by health-drink franchises. A random sample of 100 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, 100. The hypotheses that will be used by the statisticians are H_0: mu = 88,000 and H_a: mu > 88,000. Calculate the test statistic (z) that corresponds to the sample and hypotheses. Give your answer to 3 decimal places. z = __________ Using the test statistic for the Mean Corporation's hypothesis test and level a = 0.05, the Mean Corporation should _________ the null hypothesis. If the sample size is increased to 240 (but the sample mean remains unchanged), the Mean Corporation should __________ the null hypothesis.

Explanation / Answer

std error =std deviation/(n)1/2 =860

a)hence test stat =(X-mean)/std error =(89100-88000)/860=1.279

b)as for above z stat; p value=0.1004

as p value is greater then 0.05 level; we should not reject null hypothesis.

c)if sample size n=240; std error =555.128

as p value for above z stat =0.0238

as p value is less then 0.05 level; we should reject null hypothesis.

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