Question

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)			Total
	1	2	3
1	42	39	3	84
2	33	54	63	150
3	3	15	48	66
Total	78	108	114	300

(b)

Compute the expected value and variance for quality rating, x.

expected value

variance

(c)

Compute the expected value and variance for meal price, y.

expected value

variance

(d)

The

Var(x + y) = 1.6964.

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?

Since the covariance is -Select---zero positive negative , we ---Select---can can not conclude that as the quality rating increases, so does the meal price.

(e)

Compute the correlation coefficient between quality and meal price. (Round your answer to four decimal places.)

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?

The relationship between quality and meal price is ---Select---moderately positive zero moderately negative and it ---Select---is is not likely to find a low cost restaurant in this city that also has high quality.

Answer 1

b)

expected value E(x)=xP(x)=1.94

variance =(x-E(x))²*P(x)=0.4964

c)

expected value=2.12

variance =0.6256

d)

covariance of x and y =0.2872

Since the covariance is positive we can conclude that as the quality rating increases, so does the meal price.

e)

correlation coefficient between quality and meal price =0.5154

The relationship between quality and meal price is moderately positive and it not likely to find a low cost restaurant in this city that also has high quality.