Question

Past experience indicates that because of low morale, a company loses 20 hours a year per employee due to lateness and abstenteeism. Assume that the standard deviation of the population is 6 and normally distributed.

The HR department implemented a new rewards system to increase employee morale, and after a few months it collected a random sample of 20 employees and the annualized absenteeism was 14.

1. Could you confirm that the new rewards system was effective with a 90% confidence?
2. An HR subject matter expert would be very happy if the program could reduce absenteeism by 20% (i.e. to 16 hours). Given the current sampling parameters, what is the probability that the new rewards system reduced absenteeism to 16 hours and you miss it?
3. Repeat part 1) and 2) with an α = 95% CI.
4. Based on the answers in 3), is the sampling method good enough to identify a reduction from 20 to 16 hours if I use a confidence of 95%?
5. What should the sample size be if you want β to be 5%

Answer 1