Question

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

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?

What is the lower limit of this confidence interval?

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Part 2

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%.

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

2) Please select the result of your hypothesis test:

Choose the correct answer.

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

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

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

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

Result:

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? 16.08

What is the lower limit of this confidence interval? 14.20

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Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	1.9554
Sample Mean	15.1395
Sample Size	19
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.4486
Degrees of Freedom	18
t Value	2.1009
Interval Half Width	0.9424
Confidence Interval
Interval Lower Limit	14.1970
Interval Upper Limit	16.0819

Part 2

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%.

Ho: µ = 14   H₁: µ > 14

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

test-statistic = 2.5401

2) Please select the result of your hypothesis test:

Choose the correct answer.

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

3) Calculate the p-value for the hypothesis test above? P=0.0103

Excel used for calculations:

t Test for Hypothesis of the Mean
Data
Null Hypothesis                m=	14
Level of Significance	0.05
Sample Size	19
Sample Mean	15.1395
Sample Standard Deviation	1.9554
Intermediate Calculations
Standard Error of the Mean	0.4486
Degrees of Freedom	18
t Test Statistic	2.5401
Upper-Tail Test
Upper Critical Value	1.7341
p-Value	0.0103
Reject the null hypothesis