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
63
54
150
3
6
12
48
66
Total
81
114
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.
Quality
(x)
Meal Price
(y)
Total
1
2
3
1
2
3
Total
1.00
(b)
Compute the expected value and variance for quality
rating, x.
expected valuevariance
(c)
Compute the expected value and variance for meal
price, y.
expected valuevariance
(d)
The
Var(x + y)
= 1.6596.
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--- positive negative zero ,
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 ---moderately negative or moderately
positive or zero ---- and it ---is or is not ---
likley to find a low cost restaurant in this city that also
has high quality.