Chapter 9.3, Problem 15E

Federal Tax Returns. According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. 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).

1. 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.
2. 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 σ = $1600 may be assumed. What is the p-value?
3. c. At α = .05, what is your conclusion?
4. d. Repeat the preceding hypothesis test using the critical value approach.