The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating on a 3-point scale on typical meal price (1 least expensive to 3 most expensive) and quality (1 lowest quality to 3 greatest quality). A crosstabulation of the rating data is shown below. Forty-two of the restaurants received a rating of 1 on quality and 1 on meal price, 39 of the restaurants received a rating of 1 on quality and 2 on meal price, and so on. Forty-eight of the restaurants received the highest rating of 3 on both quality and meal price.
Quality (x) | Meal Price (y) 1 2 3 |
Total | ||
1 | 42 | 39 | 3 | 84 |
2 | 33 | 63 | 54 | 150 |
3 | 3 | 15 | 48 | 66 |
Total | 78 | 117 | 105 | 300 |
- a. Develop a bivariate probability distribution for quality and meal price of a randomly selected restaurant in this Canadian city. Let x = quality rating and y = meal price.
- b. Compute the
expected value and variance for quality rating, x. - c. Compute the expected value and variance for meal price, y.
- d. The Var(x + y) = 1.6691. Compute the
covariance of x and y. What can you say about the relationship between quality and meal price? Is this what you would expect? - e. Compute the
correlation coefficient between quality and meal price. What is the strength of the relationship? Do you suppose it is likely to find a low-cost restaurant in this city that is also high quality? Why or why not?
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