The sales for Sunflowers Apparel, a chain of upscale clothing stores for women, have increased during the past 12 years as the chain has expanded the number of stores open. Until now, Sunflowers managers selected sites based on subjective factors, such as the availability of a good lease or the perception that a location seemed ideal for an apparel store. As the new director of planning, you need to develop a systematic approach that will lead to making better decisions during the site selection process. As a starting point, you believe that the size of the store significantly contributes to store sales, and you want to use this relationship in the decision-making process. To examine the relationship, a sample of 14 stores was selected. The results are recorded in the accompanying table: Store Size (thousands of sq. ft) Annual Sales (millions of $) 1 1.7 3.7 2 1.6 3.9 3 2.8 6.7 4 5.6 9.5 5 1.3 3.4 6 2.2 5.6 7 1.3 3.7 8 1.1 2.7 9 3.2 5.5 10 1.5 2.9 11 5.2 10.7 12 4.6 7.6 13 5.8 11.8 14 3.0 4.1 e). At 5% level of significance, is there sufficient evidence of a linear relationship between the store size and the annual sales? [Please make sure you use Minitab and show all necessary work, with all interpretations and conclusions carefully stated.]
The sales for Sunflowers Apparel, a chain of upscale clothing stores for women, have increased during the past 12 years as the chain has expanded the number of stores open. Until now, Sunflowers managers selected sites based on subjective factors, such as the availability of a good lease or the perception that a location seemed ideal for an apparel store. As the new director of planning, you need to develop a systematic approach that will lead to making better decisions during the site selection process. As a starting point, you believe that the size of the store significantly contributes to store sales, and you want to use this relationship in the decision-making process. To examine the relationship, a sample of 14 stores was selected. The results are recorded in the accompanying table:
|
Store |
Size (thousands of sq. ft) |
Annual Sales (millions of $) |
|
1 |
1.7 |
3.7 |
|
2 |
1.6 |
3.9 |
|
3 |
2.8 |
6.7 |
|
4 |
5.6 |
9.5 |
|
5 |
1.3 |
3.4 |
|
6 |
2.2 |
5.6 |
|
7 |
1.3 |
3.7 |
|
8 |
1.1 |
2.7 |
|
9 |
3.2 |
5.5 |
|
10 |
1.5 |
2.9 |
|
11 |
5.2 |
10.7 |
|
12 |
4.6 |
7.6 |
|
13 |
5.8 |
11.8 |
|
14 |
3.0 |
4.1 |
e). At 5% level of significance, is there sufficient evidence of a linear relationship between the store size and the annual sales?
[Please make sure you use Minitab and show all necessary work, with all interpretations and conclusions carefully stated.]
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