Restaurants. The Chamber of Commerce of a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating of 1-3 on its meal price (1 = least expensive; 3 = most expensive), and quality (1 = lowest quality; 3 = greatest quality). On your sheet is a crosstabulation of the rating data.

a. Develop a bivariate probability distribution for quality and meal restaurant in this Canadian city. Let x = quality rating and y = meal price.

b. Compute the expected value for quality rating, x.

c. Compute the expected value for meal price, y.

d. The Var(x+y) = 1.6691. The Var(x) = 0.4964. The Var(y) = 0.6019. 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 the city that is also high quality? Why or why not?

Meal Price () Quality (x) i 2 3 Total 1 42 39 3 84 2 33 63 54 150 3 3 15 48 66 Total 78 117 105 300