Question

A large corporation is interested in determining whether the average days of sick leave taken annually is more for night-shift employees than for day-shift employees. It is assumed that the distribution of the days of sick leave is normal for both shifts and that the variances of sick leave taken are equal for both shifts. A random sample of 13 employees from the night shift yields an average sick leave of 11.4 days with a standard deviation of 2.2 days. A random sample of 21 employees from the day shift yields an average sick leave of 14.7 days with a standard deviation of 4.2 days.

i) At a level of significance α of 0.01, find the confidence interval for the difference between the difference of the average sick leave for the night shift and that of the day shift.

ii) In a few words, describe your conclusion about the difference between the difference of the average sick leave for the night shift and that of the day shift, based on your results from (a).

iii) Repeat part (a) for α= 0.05. Does your conclusion change about the difference between the difference of the average sick leave for the night shift and that of the day shift? Why? Why not?

Answer 1

Given that, for night shift. Let n1 =13 and for day shift.

i) C.I for difference

ii) Since C.I in part i does not include 0 value. So, there is a significant difference b/w the average of sick leave for night shifts and day shift.

ii) Now, at =0.05, then C.I becomes, then C.I become.

Since interval does not contain 0, so there is a significant difference b/w the average leave for night shift and day shift.

Therefore, there is no change in conclusion about the differenece b/w the difference of average sick leave for night and day shift.