People filing income tax returns before April 1 get a refund of $1056. Consider the population of "last-minute" filers who send their tax return during the last five days of the income tax period.

a. A researcher claims that a reason people wait till the last 5- days is that they get lower refunds than do early filers. Develop appropriate hypotheses such that rejection of H0 will support the researcher's assumption

b. For a sample of 400 individuals who filed a tax return during the last 5- days, the sample mean refund was $910. Based on prior experience a population standard deviation of = $1600 could be assumed. What is the p-value?

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

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