Individuals filing federal income tax returns prior to March 31 received an average refund of $1056. Consider the population of last-minute filers who mail their tax return "late" in April. A researcher suggests that a reason individuals wait until the last minute is that on average these individuals receive lower refunds than do early filers. For a sample of 400 individuals who filed a tax return in April, the sample mean refund was $910. The sample standard deviation was found to be s = $1600.

a. State the researcher's null and alternative hypothesis.

b. At = 0.05, test your hypothesis.

c. What is your conclusion? Explain in the context of the problem.