Question

Fresh!Now! is a chain of grocery stores in the United States with 1784 grocery stores in total, some of which also sell bakery goods and freshly made food-to-go. Fresh!Now!’s goal is to provide good quality fresh vegetables at affordable prices. However, given the existing market of organic food supplies, Fresh!Now! is facing tremendous competition. They realize that Fresh!Now! has to make their stores more attractive to customers.

In 19 stores across Massachusetts and New York, they have implemented a new concept to present the vegetables in the stores and have collected information of the average daily profit of leafy vegetables (in dollar) per customer per store (see table below). Janine, the head of the analytics department at Fresh!Now!, has tasked you with developing an anlaysis to better understand if the new concept has any effect.

Store	Profit in dollar per customer per store
MA 1	14.82
MA 2	17.15
MA 3	9.91
MA 4	13.57
MA 5	14.8
MA 6	16.49
MA 7	15.45
MA 8	14.54
MA 9	12.24
NY 1	16.59
NY 2	16.48
NY 3	14.22
NY 4	17.65
NY 5	15.84
NY 6	18.13
NY 7	13.95
NY 8	15.16
NY 9	10.94
NY 10	16.78

Store	Profit in dollar per customer per store
MA 1	14.82
MA 2	17.15
MA 3	9.91
MA 4	13.57
MA 5	14.8
MA 6	16.49
MA 7	15.45
MA 8	14.54
MA 9	12.24
NY 1	16.59
NY 2	16.48
NY 3	14.22
NY 4	17.65
NY 5	15.84
NY 6	18.13
NY 7	13.95
NY 8	15.16
NY 9	10.94
NY 10	16.78

To understand if the new concept has taken effect, you want to conduct a hypothesis test. Average daily profit per customer per store for the leafy vegetables in all other Fresh!Now! grocery stores is 13.8.

You formulate the following hypothesis test:

H0: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is not higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

H1: Average daily profit at Fresh!Now! in the New York/Massachusetts stores is higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

1) Calculate the test-statistic for the hypothesis test above.

2) Please select the result of your hypothesis test:

Choose the correct answer.

A) Fail to reject H0: You are not 95% confident that the mean profit in the Massachusetts/Boston stores is higher than the population mean. incorrect

B) Accept H0: Profit in the Massachusetts/Boston stores is lower than the population mean at the 95% confidence level.

C) Reject H0: You are 95% confident that the mean profit in the Massachusetts/Boston stores is higher than the population mean.

D) The result of your hypothesis test does not tell you if you can reject H0 or not.

3) Calculate the p-value for the hypothesis test above.

Answer 1

Since the 2.348 > 1.729, we reject the null hypothesis, as the tstat lie in the rejection region.
We conclude that Average daily profit at Fresh!Now! in the New York/Massachusetts stores is higher than the average daily profit of all other Fresh!Now! grocery stores at a confidence level of 95%.

Finding the p value for t stat, we use the t table, look at df = 19 row, and find that 2.093 is closer to our t stat and then look at the corresponding to find a p value of approx 0.025