Hypothesis testing and Confidence interval for mean using t distribution.
A hospital manager is concerned about absenteeism in its clinics. To try to decrease absence, it provides workers in Clinic A financial incentive for good attendance. No such incentive is provided in Clinic B, which has historically had almost identical absence rates to that of Clinic A.

Clinic A

Clinic B

Mean Days absent

12.3 days

18.7 days

Standard Deviation

4.4 days

5.1 days

Number of Employees

17

15

Required:
1. find out separate confidence intervals for the numbers of days absent for Clinic A and Clinic B, respectively.
2. The Health Authority is worried that if the mean days absent in either clinic reach 20 days, it will have difficulties safely operating the clinics. Conduct divides hypothesis tests for Clinics A and B (at 95% confidence) that demonstrate whether they can be confident that absence is less than 20 days.
3. Conduct a statistical test at the 5 percent level of significance to determine if the days of absence at the two clinics are significantly different from one another. Based on the sample evidence, do you think the incentive should be offered to other branches?