The Data:
Problem 3 (10 marks) In a marketing study, a company wants to study the effect of changing advertising costs spent on local TV on immediate sales of their product. The marketing department selected five levels of advertising and applied each level of spending to five communities across the country. The total sales in the following week is then measured in each community. Let X represent the cost of advertising (in thousands of $ per week) and Y represent the sales revenue (in thousands of $). The collected data is in the file ads.txt. This company treats advertising costs of over $3,000 per week as high and costs under $3,000 per week as low. Then, the revenue can be modeled as Yij = Hi + Eija Eij lid N (0,0%), where i = 1 corresponds to low advertising cost and i = 2 corresponds to high advertising cost. a. Alphonse in the marketing department wants to know if the mean revenue is the same for high and low advertising spendings. State the null and alternate hypotheses Alphonse should use. Calculate the test statistic and give the p-value of the test. State the conclusion of the hypothesis test at a = 0.05 significance level. (4 marks) b. Meanwhile, Beryl in the marketing department wants to know if the mean revenues are higher with high advertising spendings. State the null and alternate hypotheses Beryl should use. Calculate the test statistic and give the p-value of the test. State the conclusion of the hypothesis test at a = 0.05 significance value. (4 marks) c. At a department meeting, Alphonse and Beryl present their analyses. Do their findings contradict each other? Use no more than three sentences to explain why or why not. (2 marks) x,y 1.2,0. 83 1.2, 1.39 1.2, 1.12 1.2, 1.33 1.2,0. 91 2.4,0. 09 2.4, 1.53 2.4, 1.71 2.4, 1.82 2.4, 1.78 3.6,1.16 3.6,1.94 3.6,0. 93 3.6,0. 82 3.6,1.69 4.8,2.49 4.8,2.11 4.8,1.76 4.8,2. 19 4.8,2.04 Problem 3 (10 marks) In a marketing study, a company wants to study the effect of changing advertising costs spent on local TV on immediate sales of their product. The marketing department selected five levels of advertising and applied each level of spending to five communities across the country. The total sales in the following week is then measured in each community. Let X represent the cost of advertising (in thousands of $ per week) and Y represent the sales revenue (in thousands of $). The collected data is in the file ads.txt. This company treats advertising costs of over $3,000 per week as high and costs under $3,000 per week as low. Then, the revenue can be modeled as Yij = Hi + Eija Eij lid N (0,0%), where i = 1 corresponds to low advertising cost and i = 2 corresponds to high advertising cost. a. Alphonse in the marketing department wants to know if the mean revenue is the same for high and low advertising spendings. State the null and alternate hypotheses Alphonse should use. Calculate the test statistic and give the p-value of the test. State the conclusion of the hypothesis test at a = 0.05 significance level. (4 marks) b. Meanwhile, Beryl in the marketing department wants to know if the mean revenues are higher with high advertising spendings. State the null and alternate hypotheses Beryl should use. Calculate the test statistic and give the p-value of the test. State the conclusion of the hypothesis test at a = 0.05 significance value. (4 marks) c. At a department meeting, Alphonse and Beryl present their analyses. Do their findings contradict each other? Use no more than three sentences to explain why or why not. (2 marks) x,y 1.2,0. 83 1.2, 1.39 1.2, 1.12 1.2, 1.33 1.2,0. 91 2.4,0. 09 2.4, 1.53 2.4, 1.71 2.4, 1.82 2.4, 1.78 3.6,1.16 3.6,1.94 3.6,0. 93 3.6,0. 82 3.6,1.69 4.8,2.49 4.8,2.11 4.8,1.76 4.8,2. 19 4.8,2.04
