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tubalcain tubalcain
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Posts: 8
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9 years ago
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?

A.Yes, the p-value of the test for significance is less than .01.    
B.No, the sample correlation coefficient does not exceed the critical value.    
C.
Yes, the computed t-test statistic is less than the critical value.
   
D.Yes, the value of the test statistic does not exceed the critical value.
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wrote...
Valued Member
On Hiatus
9 years ago
Here is a link to the summary output from Excel ...

http://i.tinyuploads.com/dGN7Uw.jpg

 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.
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