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 (sample size of 20 and std. dev. of population. 6), what is the probability that the new rewards system reduced absenteeism to 16 hours and you miss it?
3. What should the sample size be if you want to be 5%