Expense Exercise 11.10 (Static) METHODS AND APPLICATIONS 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: Miller's $119.25 $121.32 $122.34 $120.14 $122.19 $123.71 $121.72 $122.42 $123.63 $122.44 Albert's $111.99 $114.88 $115.11 $117.02 $116.89 $116.62 $115.38 $114.40 $113.91 $111.87 Click here for the Excel Data File 124 119. 114- Albert Market Miller 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. Two-sample T for Millers vs 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 = 9.73 P-Value = 0.000 DF = 18 95% CI for difference: (5.57350, 8.64450) T-Test of diff = 0 (vs not =): T-Value Both use Pooled StDev = 1.6343 (b) Using the t statistic given on the output and critical values, test Ho versus Ha by setting a 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 = evidence. but not at a = (c) Above figure gives the p-value for testing Ho: M - HA = 0 versus Ha: M - HA 0. Use the p-value to test H versus H by setting a 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 = evidence. but not at a = (c) Above figure gives the p-value for testing Ho: M - HA = 0 versus Ha: MM - HA 0. Use the p-value to test Ho versus Ha by setting a 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 = evidence. Assessment Tool iFrame but not at a = (d-1) Above figure gives a 95 percent confidence interval for M - HA. 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 Suppose a sample of 49 paired differences that have been randomly selected from a normally distributed population of paired differences yields a sample mean of a = 4.2 and a sample standard deviation of s = 7.6. (a) Calculate a 95 percent confidence interval for Hd Assessment Tool iFrame our answers to 2 decimal places.) Answer is not complete. ] Confidence interval = [ (b) Test the null hypothesis Ho: Hd = 0 versus the alternative hypothesis Ha: Hd #0 by setting a equal to .10, .05, .01, and .001. How much evidence is there that d differs from O? |t = Reject HO at a equal to Answer is not complete. evidence that 1 differs from 2. (c) The p-value for testing Ho: Hd 3 versus Ha: Md > 3 equals 0.1373. Use the p-value to test these hypotheses with a equal to .10, .05, .01, and .001. How much evidence is there that d exceeds 3? What does this say about the size of the difference between and 2? (Round your p-value answer to 4 decimal places.) Reject HO at a equal to Answer is not complete. evidence that 1 and 2 differ by more than 3.