Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

The marketing manager of a large supermarket chain would like to use shelf space

ID: 3296493 • Letter: T

Question

The marketing manager of a large supermarket chain would like to use shelf space to predict the sales of pet food. For a random sample of 12 similar stores, she gathered the following information regarding the shelf space, in feet, devoted to pet food and the weekly sales in hundreds of dollars. Use these data to answer.

Store

1

2

3

4

5

6

Shelf Space

5

5

5

10

10

10

Weekly Sales

1.6

2.2

1.4

1.9

2.4

2.6

Store

7

8

9

10

11

12

Shelf Space

15

15

15

20

20

20

Weekly Sales

2.3

2.7

2.8

2.6

2.9

3.1



Construct a 95% prediction interval estimate for the weekly sales, in hundreds of dollars, for a store with 8 feet of shelf space devoted to pet food.

A. 2.86 < y < 6.23

B. 1.31 < y < 2.77

C. -0.131 < y < 1.84

D. 1.54 < y < 4.24

Store

1

2

3

4

5

6

Shelf Space

5

5

5

10

10

10

Weekly Sales

1.6

2.2

1.4

1.9

2.4

2.6

Explanation / Answer

answer:

What is the estimated regression equation?

Y = 1.45 + 0.074(Shelf_Space)

Is the correlation between weekly sales and shelf space significant at the .01 level of significance?

The standard error of the slope = 0.015908069

t-statistic = b /(Sb) = 0.074 / 0.015908069 = 4.651727304
p-value (10 d.f.) = 0.00091


With 12 observation, the degrees of freedom = 12 - 2 = 10. Using a t-table, the critical value is ...

critical value = 3.17

Since p < 0.01 (or equivalently, 4.651727304 > 3.17), REJECT the null. There is a significant correlation between shelf space and sales.