Answer:
The 95% confidence interval for the difference of means is (7.67, 16.33).
The estimate is Md = 12.
The standard error is sM_d = 2.176.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the difference between means.
The sample 1 (this year's sales), of size n1=36 has a mean of 53 and a standard deviation of 12.
The sample 2 (last year's sales), of size n2=49 has a mean of 41 and a standard deviation of 6.
The difference between sample means is Md=12.
The estimated standard error of the difference between means is computed using the formula:
The degrees of freedom are:
The critical t-value for a 95% confidence interval and 83 degrees of fredom is t=1.989.
The margin of error (MOE) can be calculated as:
Then, the lower and upper bounds of the confidence interval are:
The 95% confidence interval for the difference of means is (7.67, 16.33).