A survey of company executives reveals that over half of the executives feel that more work is accomplished within their companies on Tuesday than on any other day of the week. To test this claim within his own company, a health insurance company executive takes a random sample of eight employees and records the total number of claims processed by each employee over four Mondays and four Tuesdays. The following gives the recorded data:
Employee 1 2 3 4 5 6 7 8
Mondays 38 47 48 45 46 41 42 43
Tuesdays 42 46 48 54 49 47 39 49
Using the five-step format, test whether the claim that more work is accomplished on Tuesdays is correct for this company. Make sure to clearly state the null and alternative hypotheses, define the test statistic and null distribution, calculate the test statistic, find bounds the p-value, and make a conclusion in terms of the problem. (Hint: This data is paired.)
1. State H0 and Ha.
2. State α.
3. State the form of the 1 − α confidence interval you will use, along with all the assumptions necessary.
4. Calculate the 1 − α confidence interval.
5. Based on the 1 − α confidence interval, either: O Reject H0 and conclude Ha, or O Fail to reject H0.