Chapter 5.4, Problem 27E

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 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. 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

1. 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.
2. Compute the expected value and variance for quality rating, x.
3. Compute the expected value and variance for meal price, y.
4. The $Var\left(x+y\right)=1.6691$ . 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?
5. 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?