In an article titled “Airport Screeners’ Strains, Sprains Highest among Workers,” Thomas Frank reported that the injury rate for airport screeners was 29%, far exceeding the 4.5% injury rate for the rest of the federal workforce. The 48,000 full- and part-time screeners were reported to have missed nearly a quarter-million days because of injuries in the recent fiscal year.
a. Calculate the average number of days missed by airport screeners.
b. If one were to estimate the average number of days missed to within 1 hour in 2006 with a confidence level of 90%, determine the smallest sample size that would be required. Assume the standard deviation of the number of days missed is 1.5 days and that a work day consists of 8 hours.
c. How close could the estimate get if a sample of size 100 was used?