A paired-sample t-test is conducted to assess if the average net sales significantly improved after the marketing consultant's visit to five sporting goods stores in California.
To determine whether the average net sales improved after the consultant's visit, we can perform a paired-sample t-test. This statistical test compares the means of two related groups, in this case, the net sales before and after the consultant's visit for each store.
The null hypothesis (H0) assumes no improvement in average net sales after the visit, while the alternative hypothesis (H1) suggests an improvement. The level of significance (α) is set to 0.05.
Performing the paired-sample t-test on the given data, we find the t-statistic and compare it to the critical t-value for a two-tailed test with four degrees of freedom (n - 1 = 5 - 1 = 4) at α = 0.05. If the calculated t-statistic falls within the critical region, we reject the null hypothesis, indicating a significant improvement in average net sales.
After performing the calculations, if the t-statistic falls outside the critical region, we fail to reject the null hypothesis, suggesting no significant improvement.
In conclusion, the statistical analysis will provide insights into whether the consultant's visit had a significant impact on the average net sales of the sporting goods stores.
The question probable may be:
A marketing consultant was hired to visit a random sample of five sporting goods stores across the state of California. Each store was part of a large franchise of sporting goods stores. The consultant taught the managers of each store better ways to advertise and display their goods. The net sales for 1 month before and 1 month after the consultant's visit were recorded as follows for each store (in thousands of dollars):
Before visit: 57.1 94.6 49.2 77.4 43.2
After visit: 63.5 101.8 57.8 81.2 41.9
Do the data indicate that the average net sales improved? (Use a= 0.05)