Statistics - Hypothesis Testing, Coefficient of Correlation

Please see the attached file for fully formatted questions.
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Please use the 5 step hypothesis method for each problem.

1. The management of Discount Furniture, a chain of discount furniture stores in the Northeast, designed an incentive plan for salespeople. To evaluate this innovative plan, 12 salespeople were selected at random, and their weekly incomes before and after the plan were recorded.

Has the plan been effective? Use the p= .05 level. Based on your results what practical recommendations would you make to management?

2. The city of Laguna Beach operates two public parking lots. The one on Ocean Drive can accommodate up to 125 cars and the one on Rio Rancho can accommodate up to 130 cars. City planners are considering both increasing the size of the lots and changing the fee structure. To begin, the Planning Office would like some information on the number of cars in the lots at various times of the day. A junior planner officer is assigned the task of visiting the two lots at random times of the day and evening and counting the number of cars in the lots. The study lasted over a period of one month. Below is the number of cars in the lots for 25 visits of the Ocean Drive lot and 28 visits of the Rio Rancho lot.

Ocean
89 115 93 79 113 77 51 75 118 105 106 91 54
63 121 53 81 115 67 53 69 95 121 88 64
Rio Rancho
128 110 81 126 82 114 93 40 94 45 84 71 74
92 66 69 100 114 113 107 62 77 80 107 90 129
105 124

Is it reasonable to conclude that there is a difference in the mean number of cars in the two lots? Use the .05 significance level. Based upon your analysis which lot would you recommend investing in and why?

3. Shank's, Inc., a nationwide advertising firm, wants to know whether the size of an advertisement and the color of the advertisement make a difference in the response of magazine readers. A random sample of readers is shown ads of four different colors and three different sizes. Each reader is asked to give the particular combination of size and color a rating between 1 and 10. Assume that the ratings follow the normal distribution. The rating for each combination is shown in the following table (for example, the rating for a small red ad is 2).

Is there a relationship between color and size of ad. Based on your analysis is there a relationship between size and color of ad at the .05 level? If there is, what recommendation might you make to the advertising firm?

4. A sample of 12 homes sold last week in St. Paul, Minnesota, is selected. Can we conclude that as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $ thousands) also increases?

a. Compute the coefficient of correlation. Is it significant?
b. Determine the coefficient of determination. What percentage of the variation in selling price can be explained by home size?
c. Can we conclude that there is a positive association between the size of the home and the selling price? Use the .05 significance level.