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.
Exercise
The Occupational Safety and Health Administration (OSHA) mandates certain regulations that have to be adopted by corporations. Prior to the implementation of the OSHA program, a company found that for a sample of 40 randomly selected months, the mean employee time lost due to job-related accidents was 45 hours. After implementation of the OSHA program, for a random sample of 45 months, the mean employee time lost due to job-related accidents was 39 hours. It can be assumed that the variability of time lost due to accidents is about the same before and after implementation of the OSHA program (with a standard deviation being 3.5 hours).
(a) Find a 90% confidence interval for the difference in the mean time lost due to accidents.
(b) Test the hypothesis that implementation of the OSHA program has reduced the mean employee lost time. Use a level of significance of 0.10.