Question

Past experience indicates that because of low morale a company losses 20 hours a year per employee due to lateness and absenteeism. 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 16.3.

a.Could you confirm that the new rewards system was effective with a 90% confidence

b.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 (fail to reject the null)?

c.Repeat part a) and b) with an α = 95% CI.

d.Based on the answers in c), is the sampling method good enough to discriminate a reduction from 20 to 16 hours if I use a confidence of 95%?

e.What should be the sample size if you want β to be 5%, i.e. power of the test 95.

Note: this problem is very similar to Problem 11.1 seen in class. However watch out for the direction of the tails. CDF start from zero in most software's, you may need to take the complement (1-cdf%) of the cdf depending on how you frame the problem in your equations and or code.

Answer 1