A marketing research firm wishes to compare the prices charged by two supermarket chains- Miller's and Albert's.

Question:

A marketing research firm wishes to compare the prices charged by two supermarket chains- Miller's and Albert's. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain's stores. The stores for each chain are randomly selected and all purchases are made during a single week.
The shopping expenses obtained at the two chains, along with box plots of the expenses, are as follows:

Because the stores in each sample are different stores in different chains, it is reasonable to assume that the samples are indeµendent1 and we assume that weekly expenses at each chain are normally distributed.
a. Letting µM be the mean weekly expense for the shopping plan at Miller's1 and letting µA be the mean weekly expense for the shopping plan at Albert's1 Figure 10.5 gives the MINITAB output of the test of H0: µM - µA - 0 (that is1 there is no difference between µM and µA) versus Ha: µM - µA + 0 (that is1 µM and µA differ). MINITAB has employed the
MINITAB Output of Testing the Equality of Mean Weekly Expenses at Miller's and Albert's Supermarket Chains

equal variances procedure. Use the sample data to show that M = 121.92. sM = 1.40.
A = 114.811, sA = 1.841 and t = 9.73.
b. Using the t statistic given on the output and critical values, test H0 versus Ha by setting a equal to .101 .05. .011 and .001. How much evidence is there that the mean weekly expenses at Miller's and Albert's differ?
c. Figure 10.5 gives the p- value for testing H0: µM - µA = 0 versus Ha: µM- µA ‰ 0. Use the p-value to test H0 versus Ha by setting a equal to .101 .051 .011 and .001. How much evidence is there that the mean weekly expenses at Miller's and Albert's differ?
d. Figure 10.5 gives a 95 percent confidence interval for µM - µA. Use this confidence interval to describe the size of the difference between the mean weekly expenses at Miller's and Albert's. Do you think that these means differ in a practically important way?
e. Set up the null and alternative hypotheses needed to attempt to establish that the mean weekly expense for the shopping plan at Miller's exceeds the mean weekly expense at Albert's by more than $5. Test the hypotheses at the .101 .051 .011 and .001 levels of" significance. How much evidence is there that the mean weekly expense at Miller's exceeds that at Albert's by more than $5?