You may need to use the appropriate appendix table or technologyto answer this question.

Individuals filing federal income tax returns prior to March 31received an average refund of $1,053. Consider the population of\"last-minute\" filers who mail their tax return during the last fivedays of the income tax period (typically April 10 to April 15).

(a)

A researcher suggests that a reason individuals wait until thelast five days is that on average these individuals receive lowerrefunds than do early filers. Develop appropriate hypotheses suchthat rejection of

H0

will support the researcher's contention.

H0: μ > $1,053
Ha: μ ≤ $1,053H0: μ = $1,053
Ha: μ ≠ $1,053    H0: μ ≥ $1,053
Ha: μ < $1,053H0: μ < $1,053
Ha: μ ≥ $1,053H0: μ ≤ $1,053
Ha: μ > $1,053

(b)

For a sample of 400 individuals who filed a tax return betweenApril 10 and 15, the sample mean refund was $910. Based on priorexperience, a population standard deviation of

σ = $1,600

may be assumed.

What is the test statistic? (Round your answer to two decimalplaces.)

What is the p-value? (Round your answer to four decimalplaces.)

p-value =

(c)

At

α = 0.05,

what is your conclusion?

Do not reject H0. There is sufficient evidence to conclude thatthe mean refund of \"last minute\" filers is less than $1,053.RejectH0. There is sufficient evidence to conclude that the mean refundof \"last minute\" filers is less than$1,053.    Reject H0. There is insufficientevidence to conclude that the mean refund of \"last minute\" filersis less than or equal $1,053.Do not reject H0. There isinsufficient evidence to conclude that the mean refund of \"lastminute\" filers is less or equal than $1,053.

(d)

Repeat the preceding hypothesis test using the critical valueapproach.

State the null and alternative hypotheses.

H0: μ > $1,053
Ha: μ ≤ $1,053H0: μ = $1,053
Ha: μ ≠ $1,053    H0: μ ≥ $1,053
Ha: μ < $1,053H0: μ < $1,053
Ha: μ ≥ $1,053H0: μ ≤ $1,053
Ha: μ > $1,053

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

State the critical values for the rejection rule. (Use α = 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.

Do not reject H0. There is sufficient evidence to conclude thatthe mean refund of \"last minute\" filers is less than $1,053.RejectH0. There is sufficient evidence to conclude that the mean refundof \"last minute\" filers is less than$1,053.    Reject H0. There is insufficientevidence to conclude that the mean refund of \"last minute\" filersis less than or equal $1,053.Do not reject H0. There isinsufficient evidence to conclude that the mean refund of \"lastminute\" filers is less or equal than $1,053.