Individuals filing federal income tax returns prior to March 31 received and average refund of $1056. Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typically April 10 to April 15).

a. A researcher suggests that a reason individuals wait until the last five days is that on average these individuals receive lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher's contention.

b. For a sample of 400 individuals who filed a tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience a population standard deviation of ? = $1600 may be assumed. What is the p-value?

c. At a = .05 what is your conclusion?

d. Repeat the preceding hypothesis test using the critical value approach.