Question
In order to measure the effect of a storewide sales campaign on non-saleable items, the
research director of a national supermarket chain took a random sample of 13 pairs of stores which were matched according to average weekly sales volume. One store of each pair (the experimental group) was exposed to the sales campaign, while the other member of the pair (the control group) was not. The following data indicate the results over a weekly period:
|
|
Sales (in Rs. ’000) | |
|
Store |
With sales campaign |
Without sales campaign |
| 1 | 67.2 | 65.3 |
| 2 | 59.4 | 54.7 |
| 3 | 80.1 | 81.3 |
| 4 | 47.6 | 39.8 |
| 5 | 97.8 | 92.5 |
| 6 | 38.4 | 37.9 |
| 7 | 57.3 | 52.4 |
| 8 | 75.2 | 69.9 |
| 9 | 94.7 | 89 |
| 10 | 64.3 | 58.4 |
| 11 | 31.7 | 33 |
| 12 | 49.3 | 41.7 |
| 13 | 54 | 53.6 |
a) What assumption is necessary to perform the parametric test to test that there is evidence that the sales campaign has increased the sales of the items?
b) Perform the test at the 0.05 level of significance
Answer :
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Skip in 10
It looks like you have data from a study comparing sales in stores with and without a sales campaign. To analyze the effect of the sales campaign, we can perform a paired t-test to determine if there is a statistically significant difference between the two groups. ### Steps for the Analysis: 1. Calculate the differences: For each store pair, subtract the sales without the campaign from the sales with the campaign. 2. Compute the mean and standard deviation of the differences. 3. Perform a paired t-test: - Null hypothesis (\(H_0\)): The sales campaign has no effect (\(\mu_d = 0\)). - Alternative hypothesis (\(H_1\)): The sales campaign has an effect (\(\mu_d \neq 0\)). -
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