Question

In an article in the Journal of Management, Joseph Martocchio studied and estimated the costs of employee absences. Based on a sample of 176 blue-collar workers, Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. Martocchio also estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. Suppose we randomly select a sample of 100 blue-collar workers. Based on Martocchio’s estimates: (a) What is the probability that the average amount of paid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days? (Round means to 1 decimal place, standard deviations to 2 decimal places, and probabilities to 4 decimal places.) μx¯=μ σPicture Probability (b) What is the probability that the average amount of unpaid time lost during a three-month period for the 100 blue-collar workers will exceed 1.5 days? (Round standard deviations to 2 decimal places and probabilities to 4 decimal places.) μx¯=μ σPicture Probability (c) Suppose we randomly select a sample of 100 blue-collar workers, and suppose the sample mean amount of unpaid time lost during a three-month period actually exceeds 1.5 days. Would it be reasonable to conclude that the mean amount of unpaid time lost has increased above the previously estimated 1.0 days? , the probability of observing the sample is if the mean is actually 1.0.

Answer 1

a) Martocchio estimated that the mean amount of paid time lost during a three-month period was 1.4 days per employee with a standard deviation of 1.3 days. The standard deviation of the mean is The probability,

b) Martocchio estimated that the mean amount of unpaid time lost during a three-month period was 1.0 day per employee with a standard deviation of 1.8 days. The standard deviation of the mean is The probability,

c) Since the probability calculated in part (b), increases if the the mean amount of unpaid time lost has increased above the previously estimated 1.0 days, the conclusion is not reasonable.