Refer to Exercise 4-45. Suppose that the standard deviations of the values of lost time due to accidents before and after use of the OSHA program are unknown but are assumed to be equal. The first sample of size 40 gave a mean of 45 hours with a standard deviation of 3.8 hours. Similarly, the second sample of size 45, taken after the implementation of the OSHA program, yielded a mean of 39 hours with a standard deviation of 3.5 hours.
(a) Find a 95% confidence interval for the difference in the mean time lost due to job-related accidents.
(b) What assumptions are needed to answer part (a)?
(c) Can you conclude that the mean employee time lost due to accidents has decreased due to the OSHA program? Use a level of significance of 0.05.
(d) How would you test the assumption of equality of the standard deviations of time lost due to job-related accidents before and after implementation of the OSHA program? Use a level of significance of 0.05.