Answer: To determine whether the sales increase due to the coupons during the promotion is significant at the 0.01 level of significance, we can conduct a paired t-test for the differences in daily gross sales before and during the promotion.
Let's set up the hypotheses:
Null Hypothesis (H0): There is no significant difference in daily gross sales before and during the promotion (μd = 0).
Alternative Hypothesis (Ha): There is a significant difference in daily gross sales before and during the promotion (μd ≠ 0).
where μd represents the mean difference in daily gross sales before and during the promotion.
Next, we'll calculate the test statistic:
The test statistic t is calculated as follows:
t = (mean difference - hypothesized mean difference) / (standard deviation of the differences / sqrt(sample size))
Given that the standard deviation of the differences (sub D bar) is 0.616000, and the sample size is not provided, we cannot calculate the exact value of the test statistic.
To make a decision and draw a conclusion, we would compare the calculated test statistic with the critical values for a t-distribution with (n-1) degrees of freedom at the 0.01 level of significance. The degrees of freedom (df) will depend on the sample size.
If the calculated test statistic falls within the critical region (i.e., beyond the critical values), we reject the null hypothesis and conclude that there is a significant difference in daily gross sales before and during the promotion.
If the calculated test statistic falls within the non-critical region, we fail to reject the null hypothesis and conclude that there is no significant difference in daily gross sales before and during the promotion.
Without the sample size or the exact values of the daily gross sales, we cannot provide the critical values, decision, or conclusion for the test.