45 The Occupational Safety and Health Administration (OSHA) mandates certain reg

Question

45 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).

Find a 90% confidence interval for the difference in the mean time lost due to accidents.

Test the hypothesis that implementation of the OSHA program has reduced the mean employee lost time. Use a level of significance of 0.10.

Explanation / Answer

Null HYpothesis : H0 : Mean time lost due to job - related accidents are same as after implementing OSHA program as earlier.

Alternative Hypothesis : Ha : Mean time lost due to job - related accidents has been decreased after implementing OSHA program as earlier.

Sample mean After implementing OSHA program xafter = 39 months

Sample mean before implementing OSHA program xbefore = 45 months

Variability of time lost due to accidents is about the same before and after implementation of the OSHA program

with standard deviation s= 3.5 hours

so standard error of difference se0 = s * sqrt [1/n1 + 1/n2] = 3.5 * sqrt [1/40 + 1/45] = 0.761 hours

90% confidence interval = (xbefore - xafter) +- tn1+n2-2, 0.10 * se0

= (45 - 39) +- 1.6634 * 0.761

= 6 +- 1.265

= (4.735 Hours, 7.265 Hours)

THe Confidence interval doesn't consist the value of zero so that means implementation of the OSHA program has reduced the mean employee lost time.

Test Statistic

t = (xbefore - xafter)/ se0 = (45 - 39)/0.761 = 7.88

critical value of t for dF = 83 and alpha = 0.10 and for one sided tesst

tcr= 1.292

so here t > tcr so we shall reject the null hypothesis and can claim that  implementation of the OSHA program has reduced the mean employee lost time.

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