Question

The price of 30 random foods were compared between two different superstore chains. The prices for the products are shown in the accompanying data table. Complete parts (a) through (c) below. Click the icon to view the data table for the prices of the products. a. At the 0.01 level of significance, is there evidence that the mean price of items is higher at store A than at store B? Let Hy be the mean prices at store A and let Hy be the mean prices for store B. State the null and alternative hypotheses. Choose the correct answer below. - X Data table for the prices of the products O A. Ho: H0 (where Ho FH1-H2) H:Hp = 0 OC. Ho Ho 50 (where Ho = H1 - H2) H:Hp > 0 OB. Ho: Mo 20 (where Ho = H1-H2) H:Hp < 0 OD. Ho: Mo = 0 (where Ho = 11 - H2) H:Hp=0 Find the critical value(s). The critical value(s) is are) (Round to two decimal places as needed. Use a comma to separate answers as needed.) Determine the test statistic, ISTAT ISTAT-O (Round to two decimal places as needed.) State your conclusion. Product 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Store A 3.28 1.43 2.32 3.17 1.84 6.72 13.19 18.28 0.79 9.65 2.96 3.88 3.87 5.06 3.41 1.25 2.99 2.96 2.95 1.46 3.95 1.61 1.32 1.33 1.03 0.85 3.94 2.92 3.64 1.22 Store B 2.58 1.99 2.97 1.97 4.77 5.18 9.08 16.97 1.48 13.43 2.55 4.04 3.39 4.85 3.77 1.25 2.98 1.94 2.49 1.11 3.73 1.60 1.31 2.24 1.16 0.98 4.05 2.45 1.81 0.88 Ho. There evidence to conclude that the mean price of the warehouse club purchases is greater than the store-brand purchases. b. What assumption is necessary about the population distribution in order to perform this test? O A. It must be assumed that the distribution of the differences between the prices is approximately normal. OB. It must be assumed that the distribution of the differences between the prices is skewed. OC. It must be assumed that the distribution of the differences between the prices is approximately uniform. c. Find the p-value in (a) and interpret its meaning. The test statistic gives a p-value of (Round to three decimal places as needed.) Interpret the meaning of the p-value in (a). Choose the correct answer below. Print Done O A. The p-value is the probability of failing to reject the null hypothesis when it is actually false. OB. The p-value is the probability of obtaining a sample mean difference at least as extreme as this one if the population mean prices between the stores are the same. O c. The p-value is the probability of obtaining a sample mean difference less extreme than this one if the population mean prices between the stores are different.

Answer 1

briven dataset: product stone A (X) Store B (x2) Dibb (B) = (x,- x) 1 3.28 2.58 0.7 2 1.43 199 -0.56 3 2.32 2.97 - 8.65 4 3.17 1.97 1.84 4.77 -2.93 6.72 5:18 1.54 13.19 9.08 4 H 8. 18. 28 16.97 1:31 0.79 148 -0.69 10 9.65 13.43 -3.78 2.96 2.55 0.41 12, 3.88 4.04 -o. 16 13, 3.87 3.39 0.48 5.06 4.85 Ou21 15. 3.41 3.77 0.36 16. 1.25 1.25 17. 2.99 2.99 18. 2.96 1.94 1.02 19. 2.95 2.49 0.46 20 1.46 0.35 21. 3.95 3.73 0.22 22 23. 1.32 1031 0.01 24. 1.33 2.24 -0.91 25 1.03 1.16 -0.13 26 6085 27 3.94 2 92 3.66 28 4.05 2.45 1.81 -0.13 -0.11 Oo 47 1.8.3

30 - 88 0.34 1.22 Average (X) = 0.1423 Standard deviation n-1 ID n I 29 1 29 (53.5 3.5757 - 30X0.02026) 1.3515 (so) Here we 30 we random foods bor once stone B. we conduct paired to test. select and kept them in stone A and again we kept the same collected data are not to each other. 30 so product in independent Hypot thesis! a), Ho 24.co Hi! Horo one tooled test Cuppen tooled) This is the critical value is ta, not t 0.01, 29 -2.462 N 2.46 t 7 - Mo SAAT tn-l Solin 0.1423-0 - 0.5767. ř 0.57. 1-3515/130

AS tatat < tonitical Don't reject Ho, Ho, There is no subficient evidence to conclude that the mean price of ware house clube purchases is greater than the store brand purchases A b . e . The test statistic gives a a paralue ob 0.286 interpret the meaning of the p-value in (a). B N. B p-value is results from as entreme the is the probability of getting data the observed results of hypothesis when the null hypothesis is assumed test, to be correct,
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