Expected Price	Promotion
3.78	1
3.82	1
4.18	1
4.46	1
4.31	1
4.56	1
4.36	1
4.54	1
3.89	1
4.13	1
3.97	1
4.38	1
3.98	1
3.91	1
4.34	1
4.24	1
4.22	1
4.32	1
3.96	1
4.73	1
3.62	1
4.27	1
4.79	1
4.58	1
4.46	1
4.18	1
4.4	1
4.36	1
4.37	1
4.23	1
4.06	1
3.86	1
4.26	1
4.33	1
4.1	1
3.94	1
3.97	1
4.6	1
4.5	1
4	1
4.12	3
3.91	3
3.96	3
4.22	3
3.88	3
4.14	3
4.17	3
4.07	3
4.16	3
4.12	3
3.84	3
4.01	3
4.42	3
4.01	3
3.84	3
3.95	3
4.26	3
3.95	3
4.3	3
4.33	3
4.17	3
3.97	3
4.32	3
3.87	3
3.91	3
4.21	3
3.86	3
4.14	3
3.93	3
4.08	3
4.07	3
4.08	3
3.95	3
3.92	3
4.36	3
4.05	3
3.96	3
4.29	3
3.6	3
4.11	3
3.32	5
3.86	5
4.15	5
3.65	5
3.71	5
3.78	5
3.93	5
3.73	5
3.71	5
4.1	5
3.69	5
3.83	5
3.58	5
4.08	5
3.99	5
3.72	5
4.41	5
4.12	5
3.73	5
3.56	5
3.25	5
3.76	5
3.56	5
3.48	5
3.47	5
3.58	5
3.76	5
3.57	5
3.87	5
3.92	5
3.39	5
3.54	5
3.86	5
3.77	5
4.37	5
3.77	5
3.81	5
3.71	5
3.58	5
3.69	5
3.45	7
3.64	7
3.37	7
3.27	7
3.58	7
4.01	7
3.67	7
3.74	7
3.5	7
3.6	7
3.97	7
3.57	7
3.5	7
3.81	7
3.55	7
3.08	7
3.78	7
3.86	7
3.29	7
3.77	7
3.25	7
3.07	7
3.21	7
3.55	7
3.23	7
2.97	7
3.86	7
3.14	7
3.43	7
3.84	7
3.65	7
3.45	7
3.73	7
3.12	7
3.82	7
3.7	7
3.46	7
3.73	7
3.79	7
3.94	7

Transcribed Image Text:

If a supermarket product is offered at a reduced price frequently, do customers expect the price of the product to be lower in the future? This question is important from a marketing perspective since profits are directly affected by sale promotion policies. This question was examined by researchers in a study conducted on students enrolled in a management faculty at a large Canadian university. For 10 weeks, 160 subjects received information about the products. The treatment conditions corresponded to the number of promotions (1, 3, 5 or 7) that were distributed during this 10-week period. Students were randomly assigned to 4 groups. Data on expected prices for the different groups can be found in the Assig3_Question 1.mtw and Assig3_Data.xlsx data files. (a) Is this an observational study or a designed experiment? Explain briefly [1 Mark] (b) The researchers want to test the impact of the frequency of promotions on the expected price. State the appropriate null and alternative hypotheses. [1 Marks] (c) Make a boxplot of the data and the usual 4 residual plots and explain with reference to the appropriate plot (s) whether the key assumptions of the ANOVA model are justified. [2 Marks] (d) Fill in the correct values for the missing quantities in the ANOVA table below. Show your computations (maximum of 2 decimal places). [5 Marks] Analysis of Variance DF Adj SS Adj MS F-Value P-Value Source Promotion 3 X X X X Error X 0.061 Total 159 20.53 (e) Using software, calculate the sample mean and sample standard deviation for each sample. Then use the sample standard deviations to calculate the pooled variance manually. Check to see if your pooled variance agrees with the MSE from the ANOVA Output. [2 Marks] (f) Test the null hypothesis of no difference in the true mean expected price for the four groups. Use a = 0.05 and the critical value approach. What conclusion can be drawn? (Make sure to show all the steps) [4 Marks] (g) Use the Tukey multiple comparison method in Minitab to determine which population means differ at a = 0.05. [2 Marks] (h) Use the Kruskal Wallis nonparametric test to determine whether there is difference among the median expected price among the four group. You can use Minitab for the computations but remember to show all the steps of your analysis and to use the critical value approach for your decision. Are your conclusions consistent with your results in f) above? Explain briefly. [3 Marks] If a supermarket product is offered at a reduced price frequently, do customers expect the price of the product to be lower in the future? This question is important from a marketing perspective since profits are directly affected by sale promotion policies. This question was examined by researchers in a study conducted on students enrolled in a management faculty at a large Canadian university. For 10 weeks, 160 subjects received information about the products. The treatment conditions corresponded to the number of promotions (1, 3, 5 or 7) that were distributed during this 10-week period. Students were randomly assigned to 4 groups. Data on expected prices for the different groups can be found in the Assig3_Question 1.mtw and Assig3_Data.xlsx data files. (a) Is this an observational study or a designed experiment? Explain briefly [1 Mark] (b) The researchers want to test the impact of the frequency of promotions on the expected price. State the appropriate null and alternative hypotheses. [1 Marks] (c) Make a boxplot of the data and the usual 4 residual plots and explain with reference to the appropriate plot (s) whether the key assumptions of the ANOVA model are justified. [2 Marks] (d) Fill in the correct values for the missing quantities in the ANOVA table below. Show your computations (maximum of 2 decimal places). [5 Marks] Analysis of Variance DF Adj SS Adj MS F-Value P-Value Source Promotion 3 X X X X Error X 0.061 Total 159 20.53 (e) Using software, calculate the sample mean and sample standard deviation for each sample. Then use the sample standard deviations to calculate the pooled variance manually. Check to see if your pooled variance agrees with the MSE from the ANOVA Output. [2 Marks] (f) Test the null hypothesis of no difference in the true mean expected price for the four groups. Use a = 0.05 and the critical value approach. What conclusion can be drawn? (Make sure to show all the steps) [4 Marks] (g) Use the Tukey multiple comparison method in Minitab to determine which population means differ at a = 0.05. [2 Marks] (h) Use the Kruskal Wallis nonparametric test to determine whether there is difference among the median expected price among the four group. You can use Minitab for the computations but remember to show all the steps of your analysis and to use the critical value approach for your decision. Are your conclusions consistent with your results in f) above? Explain briefly. [3 Marks]

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Solution a This is a designed experiment as the students in the ... View the full answer