The routes of postal deliverers are carefully planned so that each deliverer works between 7 and 7.5 hours per shift. The planned routes assume an average walking speed of 2 miles per hour and no shortcuts across lawns. In an experiment to examine the amount of time deliverers actually spend completing their shifts, a random sample of 75 postal deliverers was secretly timed.
a. Estimate with 99% confidence the mean shift time for all postal deliverers.
b. Check to determine whether the required condition for this statistical inference is satisfied.
c. Is there enough evidence at the 10% significance level to conclude that postal workers are on average spending less than 7 hours per day doing their jobs?