Question: A marketing research firm wishes to compare the prices charged by two supermarket chains, say Market A and B. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores are randomly selected, and all purchases are made during a single week.

a) Using a 0.05 level of significance, do you believe that Market A is charging more than Market B? Please state your hypothesis(s) clearly (both verbally and symbolically). Also briefly explain the testing procedure(s) (namely what type of test(s) you will be using, how you would calculate your test statistic, p-value and the rejection criteria).

PS: Relevant outputs are given below, please refer to them in order to answer the above problem.

Test Results for Unequal Variances

Test F Ratio Prob > F

Ratio of Sample Variances 1.7323 0.4255

t’ Test results for independent samples t-test

A-B

Assuming unequal variances (Case 2)

Difference 7.10900 t Ratio ?

Std Err Dif 0.73087 DF 16.7936

Upper CL Dif 8.65245 Prob > |t| ?

Lower CL Dif 5.56555 Prob > t ?

Confidence 0.95 Prob < t ?

t Test results for independent samples t-test

A-B

Assuming equal variances (Case 1)

Difference 7.10900 t Ratio ?

Std Err Dif 0.73087 DF 18

Upper CL Dif 8.64450 Prob > |t| ?

Lower CL Dif 5.57350 Prob > t ?

Confidence 0.95 Prob < t ?

Matched Pairs t-test results

Difference: B-A

Column 4 114.807 t-Ratio ?

Column 3 121.916 DF 9

Mean Difference -7.109 Prob > |t| ?

Std Error 0.66573 Prob > t ?

Upper95% -5.603 Prob < t ?

Lower95% -8.615

N 10

b) What assumption(s) do you need to make in order answer the above questions?