A marketing research firm wishes to compare the prices charged
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 independent, 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’s, and letting μA be the mean weekly expense for the shopping plan at Albert’s, Figure 10.5 on the next page gives the MINITAB output of the test of H0: μM – μA = 0 (that is, there is no difference between μM and μA) versus Ha: μM – μA ≠ 0 (that is, μM and μA differ). Note that MINITAB has employed the equal variances procedure. Use the sample data to show that x-barM = 114.81, sA =1.84, and t = 9.73.
b. Using the t statistic given on the output and critical values, test H0 versus Ha by setting equal to .10, .05, .01, 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 α equal to .10, .05, .01, 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 .10, .05, .01, 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?
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