You may need to use the appropriateappendix tableortechnologyto answer this question.

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,059. 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.

A)H₀:= $1,059H_a:$1,059

B) H₀:< $1,059H_a:$1,059

C)H₀:$1,059H_a:< $1,059

D) H₀:> $1,059H_a:$1,059

E) H₀:$1,059H_a:> $1,059

(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= $1,600may 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?

A)RejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059.

B)RejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.

C)Do not rejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059.

D)Do not rejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.

(d)

Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses.

A)H₀:= $1,059H_a:$1,059

B)H₀:< $1,059H_a:$1,059

C)H₀:$1,059H_a:< $1,059

D)H₀:> $1,059H_a:$1,059

E)H₀:$1,059H_a:> $1,059

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 statistic_____

test statistic_________

State your conclusion.

A)RejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059.

B)RejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.

C)Do not rejectH₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059.

D)Do not rejectH₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.