The marketing manager of a large supermarket chain would like to use shelf space
ID: 3428982 • 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. .
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
Is the correlation between weekly sales and shelf space significant at the .01 level of significance?
Yes, the computed t-test statistic is less than the critical value.
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
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.
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