Question

In: Statistics and Probability

Fresh!Now! is a chain of grocery stores in the United States with 1921 grocery stores in...

Fresh!Now! is a chain of grocery stores in the United States with 1921 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 16.4
MA 2 17.16
MA 3 10.19
MA 4 13.28
MA 5 15.59
MA 6 15.51
MA 7 15.61
MA 8 14.09
MA 9 12.49
NY 1 16.18
NY 2 17.14
NY 3 14.24
NY 4 17.25
NY 5 15.2
NY 6 17.25
NY 7 14.69
NY 8 15.85
NY 9 12.45
NY 10 17.08

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.

What is the upper limit of this confidence interval?

Round your answer to three decimals places (e.g. if your calculation results in 12.9237 put in 12.924).

2. What is the lower limit of this confidence interval?

Round your answer to three decimals places (e.g. if your calculation results in 12.9237 put in 12.924)..

3. 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 14.

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%.

Calculate the test-statistic for the hypothesis test above.

Solutions

Expert Solution

Solution

1)

What is the upper limit of this confidence interval?

1.089

2. What is the lower limit of this confidence interval?

-2.595

3)

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%.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the 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%.

orchestra answered 1 year ago
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