A marketing research rm 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: Miller's $119.25 $121.32 $122.34 $129.14 $122.19 $123.?1 $121.22 $122.42 $123.53 $122.44 Albert's $111.99 $114.88 $115.11 $11?.82 $116.89 $116.52 $115.38 $114.46 $113.91 $111.8? Click here for the Excel Data File 124 Expense 114 Albert Miller Market Because the stores in each sample are different stores in different chains, 'rt is reasonable to assume that the samples are independent, and we assume that weekly expenses at each chain are normally distributed. Two-sample T for Millers ys Alberts N Mean StDev SE Mean Millers 10 121.92 1.40 0.44 Alberts 10 114. 81 1.84 0.58 Difference = (Millers ) - #(Alberts) Estimate for difference: 7.10900 95% CI for difference: (5. 57350, 8. 64450) T-Test of diff = 0 (vs not =) : T-Value = 9.73 P-Value = 0.000 DF = 18 Both use Pooled StDev = 1.6343 (b) Using the t statistic given on the output and critical values, test H versus H, by setting of equal to 10, .05, .01, and .001. How much evidence is there that the mean weekly expenses at Miller's and Albert's differ? (Round your answer to 2 decimal places.) t = Reject HO at a = but not at a = evidence. (c) Above figure gives the p-value for testing He : AM - HA = 0 versus Ha : AM - MA # 0. Use the p-value to test Ho versus Ha by setting of equal to 10, .05, 01, and .001. How much evidence is there that the mean weekly expenses at Miller's and Albert's differ? p-value = Reject HO at a = but not at a = evidence.(d-1) Above figure gives a 95 percent confidence interval for AM - MA- Use this confidence interval to describe the size of the difference between the mean weekly expenses at Miller's and Albert's. (Round your answers to 2 decimal places.) The mean weekly expenses differ between and (d-2) Do you think that these means differ in a practically important way? O Not probably O Probably (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? (Round your answer so to 4 decimal places and t-value to 3 decimal places.) HO: UM - JA versus Ha: UM - JA $2p = 2.6728 t = 2.886 Reject H0 at a = but not at a = evidence