Question

Because of the pandemic, Wegman’s wants to expedite their grocery services by reorganizing so that people do not have to spend as much time in their store each visit. They sample random customers to see how long they spend shopping at the store. After reorganizing, they measure how long those same customers take in the grocery store.

Your data show the following for a sample of 16 customers.

Minutes Spent Shopping	Before Reorganization	After Reorganization	Difference
Mean	43.2	37.9	5.3
Standard Deviation	10.3	9.0	7.8

a. Wegmans hires you to determine how successful their reorganization was. Did the reorganization reduce the amount of time customers shop in the store? Set up, conduct, and interpret a hypothesis test to answer this question based on a Type-I error rate of 0.01.

b. The p-value for this test was found to be about 0.008, explain what that means.

c. What assumption do you need to make in order for this test to be valid? Be specific.

  

Answer 1

(a)

Here time spent in shopping in two different instances were observed. So, we have to perform paired t-test.

We have to test for null hypothesis

against the alternative hypothesis

Our test statistics is given by

Here,

Number of pairs of observation

Degrees of freedom

Corresponding [Using R-code '1-pt(2.717949,15)']

Level of significance

We reject our null hypothesis if .

Here, we observe that .

So, we reject our null hypothesis.

Hence, based on the given data we can conclude that there is significance decrease in time spent in shopping and so the reorganization was successful.

(b)

P-value = 0.008. It means that probability that the time spent was more after reorganization than that before reorganization is 0.008.

(c)

We assumed that same customer shopped once before reorganization and once after reorganization.