The Bureau of Labor Statistics, U.S. Office of Personnel Management, indicated that the average hourly compensation (salary plus benefits) for federal workers (not including military or postal service employees) was $44.82. The rates for private industry and state and local government workers are believed to be considerably less than that. The file titled Paychecks contains a random sample of the hourly amounts paid to state and local government workers.
a. If the hourly compensation for federal workers was normally distributed, determine the median hourly compensation.
b. Calculate the sample proportion of the state and local government workers whose hourly compensation is less than $44.82.
c. If a sample of size 150 was obtained from a population whose population proportion was equal to your answer to part a, determine the probability that the sample proportion would be equal to or greater than the answer obtained in part b.
d. On the basis of your work in parts a, b, and c, would you conclude that the proportion of state and local workers whose hourly compensation is less than $44.82 is the same as that of the federal workers? Explain.