ou may need to use the appropriate appendix table or technology to 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 last five days of the income tax period (typically April 10 to April 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: ?= $1,059 Ha: ? ≠ $1,059  B) H0: ?< $1,059 Ha: ?≥ $1,059     C) H0: ? ≥ $1,059  Ha: ? < $1,059  D) H0: ?> $1,059 Ha: ? ≤ $1,059  E) H0: ?≤ $1,059 Ha: ? > $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 the p-value? (Round your answer to four decimal places.) p-value =     (c) At ? = 0.05,what is your conclusion? Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059. Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.     Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059. Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.

You may need to use the appropriate appendix table or technology to 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 last five days of the income tax period (typically April 10 to April 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.

1. A) H₀: ?= $1,059 H_a: ? ≠ $1,059 
2. B) H₀: ?< $1,059 H_a: ?≥ $1,059    
3. C) H₀: ? ≥ $1,059  H_a: ? < $1,059 
4. D) H₀: ?> $1,059 H_a: ? ≤ $1,059 
5. E) H₀: ?≤ $1,059 H_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 the p-value? (Round your answer to four decimal places.)

p-value =  

(c)

At ? = 0.05,what is your conclusion?

1. Reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059.
2. Reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.   
3.  Do not reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059.
4. Do not reject H₀. 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.

1. H₀: ?= $1,059 H_a: ? ≠ $1,059 
2. H₀: ?< $1,059 H_a: ? ≥ $1,059      
3. H₀: ?≥ $1,059 H_a: ? < $1,059 
4. H₀: ?> $1,059 H_a: ? ≤ $1,059 
5. 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.

1. Reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,059.
2. Reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.    
3.  Do not reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,059.
4. Do not reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,059.