Question

This Question has 6 parts a) to f): Answer all of them below:

A local wine manufacturer in Pennsylvania has designed a new package for its existing product and wants to test its effectiveness using a field experiment. The manufacturer knows that for the old package, the average sales per day in State College is $4,000 and the average sales per day in Lancaster is $6,000. The manufacturer launched field experiments in wine shops at two areas: State College and Lancaster. During the one-month test period (25 days), the average sales per day in State College and Lancaster are recorded. For all the problems, we assume the significance level is 0.05.

The branch manager Tom at State College wants to know whether the average sales using the new package is different from that using the old package. He developed the following hypothesis:

H_0:μ=4000

H_a:μ≠4000

μ is the average sales per day in State College with the new package.

During the one-month test period (25 days), the average sales per day in State College is $4,250 with a standard deviation of $800.

a) Calculate the Z-statistic for the hypothesis above

b) Using SPSS, you found the p-value for the two-sided test in a) is 0.059. What statistical decision will you make based on the p-value.

c) After looking at your analysis, Tom said

“Since I already know the sample average sales 4,250$ for the new package is higher than the average sales for the old package 4,000$, I should be using a one-sided test instead of a two-sided test”.

Based on what Tom said, formulate the revised null and alternative hypothesis (one-sided).

During the one-month test period (25 days), the average sales per day in Lancaster is $6,100 with a standard deviation of $600.

The branch manager Sam at Lancaster wants to know whether the average sales using the new package is different from that using the old package. He developed the following hypothesis:

H_0:μ=6000

H_a:μ≠6000

μ is the average sales per day in Lancaster with the new package.

d) Calculate the Z-statistic for the hypothesis above

e) Compute the probability associated with the z statistic calculated in d) ( Tip: use excel formula 1-NORM.S.DIST(z,TRUE))

f) Based on your answer in e), what statistical decision will you make? Are you going to reject this null hypothesis?

Answer 1