Item WinCo Foods Walmart Bananas (lb) $0.42 $0.48 Red Onions (lb) $0.58 $0.98 Mini Peeled Carrots (1 lb bag) $0.98 $1.48 Roma Tomatoes (lb) $0.98 $2.67 Deli Tater Wedges (lb) $1.18 $1.78 Beef Cube Steak (lb) $3.83 $4.11 Beef Top Round London Broil (lb) $3.48 $4.12 Pillsbury Devils Food Cake Mix (18.25 oz) $0.88 $0.88 Lipton Rice and Sauce Mix (5.6 oz) $0.88 $1.06 Sierra Nevada Pale Ale (12 - 12 oz bottles) $12.68 $11.84 GM Cheerios Oat Clusters (11.3 oz) $1.98 $2.74 Charmin Bathroom Tissue (12 roll) $5.98 $5.48 Bumble Bee Pink Salmon (14.75 oz) $1.58 $1.98 Pace Thick & Chunky Salsa, Mild (24 oz) $2.28 $2.78 Nalley Chili, Regular w/Beans (15 oz) $0.78 $0.78 Challenge Butter (lb quarters) $2.18 $2.58 Kraft American Singles (12 oz) $2.27 $2.27 Yuban Coffee FAC (36 oz) $5.98 $7.56 Totino's Pizza Rolls, Pepperoni (19.8 oz) $2.38 $2.42 Rosarita Refried Beans, Original (16 oz) $0.68 $0.73 Barilla Spaghetti (16 oz) $0.78 $1.23 Sun-Maid Mini Raisins (14 - 0.5 oz) $1.18 $1.36 Jif Peanut Butter, Creamy (28 oz) $2.54 $1.92 Dole Fruit Bowl, Mixed Fruit (4 - 4 oz) $1.68 $1.98 Progresso Chicken Noodle Soup (19 oz) $1.28 $1.38 Precious Mozerralla Ball, Part Skim (16 oz) $3.28 $4.23 Mrs. Cubbison Seasoned Croutons (6 oz) $0.88 $1.12 Kellog's Raisin Bran (20 oz) $1.98 $1.68 Campbell's Soup at Hand, Cream of Tomato (10.75 oz) $1.18 $1.26 WinCo Foods, a large discount grocery retailer in the Western United States, promotes itself as the lowest priced grocery retailer. In newspaper ads WinCo Foods published a price comparison for products between WinCo and several competing grocery retailers. One of the retailers compared against WinCo was Walmart, also known as a low price competitor. WinCo selected a variety of products, listed the price of the product charges at each retailer, and showed the sales receipt to prove the prices at WinCo were the lowest in the area. A sample of the products and their price comparison at both WinCo and Walmart are shown on the left. Do the prices listed indicate that, on average, prices at WinCo are lower than prices at Walmart? Use 5% significance level. Solve this question using Excel. State the null & alternative hypotheses clearly. Interpret the Excel output and state your conclusion clearly. Provide all your results and comments on this sheet. Specifically, type in your answers in the spaces provided below: Are the samples related (i.e. dependent) or independent? Null Hypothesis: Alternative Hypothesis: Interpretation of Excel output: Full conclusion: Branch 1 4.21 5.55 3.02 5.13 4.77 2.34 3.54 3.20 4.50 6.10 0.38 5.12 6.46 6.19 3.79 Branch 2 9.66 5.90 8.02 5.79 8.73 3.82 8.01 8.35 10.49 6.68 5.64 4.08 6.17 9.91 5.47 A bank with a branch (Branch 1) located in a commercial district of a city has developed an improved process for serving customers during the noon-to-1 p.m. lunch period. The waiting time (operationally defined as the time elapsed from when the customer enters the line until he or she reaches the teller window) needs to be shortened to increase customer satisfaction. A random sample of 15 customers is selected and the results (in minutes) are shown in the table on the left. In addition, suppose that another branch (Branch 2), located in a residential area, is also concerned with the noon-to-1 p.m. lunch period. A random sample of 15 customers is selected and the results are shown in the table on the left. Assuming that the population variances from both branches are equal, is there evidence of a significant difference in the mean waiting time between the two branches? Use alpha = 0.01. Solve this question using Excel. State the null & alternative hypotheses clearly. Interpret the Excel output and state your conclusion clearly. Provide all your results and comments on this sheet. Specifically, type in your answers in the spaces provided below: Are the samples related (i.e. dependent) or independent? Null Hypothesis: Alternative Hypothesis: Interpretation of Excel output: Full conclusion: Men $107.48 $143.61 $90.19 $125.53 $70.79 $83.00 $129.63 $154.22 $93.80 $110.42 Women $125.98 $45.53 $56.35 $80.62 $46.37 $44.34 $75.21 $68.48 $85.84 $126.11 Some studies have shown that in the United States, men spend more than women buying gifts and cards on Valentine's Day. Suppose a researcher wants to test this hypothesis by randomly sampling 10 men and 10 women with comparable demographic characteristics from various large cities across the United States to be in a study. Each study participant is asked to keep a log beginning one month before Valentine's Day and record all purchases made for Valentine's Day during that one-month period. The resulting data are shown below. Use these data and a 1% level of signicance to test to determine if, on average, men actually do spend signicantly more than women on Valentine's Day. Assume that such spending is normally distributed in the population and that the population variances are equal. Solve this question using Excel. State the null & alternative hypotheses clearly. Interpret the Excel output and state your conclusion clearly. Provide all your results and comments on this sheet. Specifically, type in your answers in the spaces provided below: Are the samples related (i.e. dependent) or independent? Independent Null Hypothesis: u <0 alternative hypothesis: u> 0 Interpretation of Excel output: reject null hypothesis t-Test: Two-Sample Assuming Equal Variances Men Women Mean 110.867 75.483 Variance 736.874 930.724 10 10 Observations Pooled Variance Hypothesized Mean D df t Stat P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail 833.7993566667 0 18 2.74 0.0067 2.55 0.0135 2.8784404727 Full conclusion: Since T-observed (2.74) is more extreme to the left than t-critical (2.55) , we reject the null hypothesis. The evidence concludes that we do not give enough evidencemen do spend more than women for Valentines. WORKER 1 2 3 4 5 WEDNESDAY OUTPUT FRIDAY OUTPUT 71 53 56 47 75 52 68 55 74 58 In manufacturing, does worker productivity drop on Friday? In an effort to determine whether it does, a company's personnel analyst randomly selects from a manufacturing plant ve workers who make the same part. He measures their output on Wednesday and again on Friday and obtains the following results. The analyst uses alpha = 0.05 and assumes the difference in productivity is normally distributed. Do the samples provide enough evidence to show that productivity drops on Friday? Solve this question using Excel. State the null & alternative hypotheses clearly. Interpret the Excel output and state your conclusion clearly. Provide all your results and comments on this sheet. Specifically, type in your answers in the spaces provided below: t-Test: Paired Two Sample for Means Are the samples related (i.e. dependent) or independent? Dependent WEDNESDAY OUTPUT FRIDAY OUTPUT Null Hypothesis: D<0 Mean 68.8 53 Variance 58.7 16.5 5 5 Observations Pearson Correlation 0 df 4 P(T<=t) one-tail t Critical one-tail P(T<=t) two-tail t Critical two-tail Interpretation of Excel output: Reject null hypothesis. P-value (0.0026)< alpha (0.05) 0.763137142 Hypothesized Mean Difference t Stat Alternative Hypothesis:D>0 6.71 0.0013 2.13 0.0026 2.78 Full conclusion: Since T-obs (6.71) is more extreme than T-crit (2.13), we will reject Ho. The evidence concludes that the productivity level drops on Fridays