Problem 1 - Fresh!Now!

Part 1

Fresh!Now! is a chain of grocery stores in the United States with 1184 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). Louise, 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	15.86
MA 2	17.1
MA 3	11.08
MA 4	13.2
MA 5	14.59
MA 6	15.85
MA 7	15.69
MA 8	14.22
MA 9	12.34
NY 1	15.93
NY 2	16.5
NY 3	15.59
NY 4	17.57
NY 5	15.81
NY 6	18.94
NY 7	13.08
NY 8	16.12
NY 9	10.75
NY 10	16.1

Your first task it to create a 95% confidence interval for the mean of the dataset using the sample collected from Massachusetts and New York.

Q1)What is the upper limit of this confidence interval?

Q2) What is the lower limit of this confidence interval?

Part 2

To understand if the new concept has taken effect, Irene Watson, the head of the analytics department, asks you to conduct a hypothesis test. Average daily profit per customer per store for the leafy vegetables in all other Fresh!Now! grocery stores is 13.9.

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%.

Q1)Calculate the test-statistic for the hypothesis test above.

Q2) Calculate the p-value for the hypothesis test above.