Individuals filing federal income tax returns prior to March 31 received an average refund of $1,048. Consider the population of "last-minute" filers who mail their tax return during the lastfive daysof the income tax period (typicallyApril 10toApril 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.

H₀: < $1,048 H_a: $1,048

H₀: $1,048 H_a: > $1,048

H₀: > $1,048 H_a: $1,048

H₀: = $1,048 H_a: $1,048

H₀: $1,048 H_a: < $1,048

(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 = $1,600 may be assumed .

- What is the test statistic? (Round your answer to two decimal places.)

- What is thep-value?(Round your answer to four decimal places.)p-value =

(c)At = 0.05, what is your conclusion?

- RejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,048.

- Do not rejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,048.

- Do not rejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,048.

- RejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,048.

(d)Repeat the preceding hypothesis test using the critical value approach.State the null and alternative hypotheses.

H₀:< $1,048 H_a:$1,048

H₀:$1,048 H_a:> $1,048

H₀:> $1,048 H_a:$1,048

H₀:= $1,048 H_a:$1,048

H₀:$1,048 H_a:< $1,048

Find the value of the test statistic. (Round your answer to two decimal places.)

State the critical values for the rejection rule. (Use= 0.05. Round your answer to two decimal places. If the test is one-tailed, enter NONE for the unused tail.)test statistictest statisticState your conclusion.

- RejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,048.

- Do not rejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,048.

- Do not rejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,048.

- RejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,048.