Question

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.

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.

Calculate the Z-statistic for the hypothesis above.

Answer 1