Question

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,057. 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: μ < $1,057
H_a: μ ≥ $1,057

b.H₀: μ ≥ $1,057

H_a: μ < $1,057    

c. H₀: μ = $1,057
H_a: μ ≠ $1,057

d.H₀: μ > $1,057
H_a: μ ≤ $1,057

e. H₀: μ ≤ $1,057
H_a: μ > $1,057

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 σ = $1,600 may 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.)

c.At α = 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 $1,057.

Do not reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,057.     

Do not reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,057.

Reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,057.

d.Repeat the preceding hypothesis test using the critical value approach.

State the null and alternative hypotheses.

a.H₀: μ < $1,057
H_a: μ ≥ $1,057

b.H₀: μ ≥ $1,057
H_a: μ < $1,057     

c.H₀: μ = $1,057
H_a: μ ≠ $1,057

d.H₀: μ > $1,057
H_a: μ ≤ $1,057

e.H₀: μ ≤ $1,057
H_a: μ > $1,057

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

Reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,057.

Do not reject H₀. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,057.     

Do not reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,057.

Reject H₀. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,057.

Answer 1

a. Develop appropriate hypotheses such that rejection of Ho will support the researcher's contention.

b.

Ho :

Ha :

Sample size : Number of individuals who filed taxes return between April 10 and 15 : n = 400

sample mean refund : =  $910

Population Standard deviation of = $1,600

Hypothesized mean : = 1057

Test statistic = -1.84

For left tailed test :

p value = 0.0331

c.At = 0.05, what is your conclusion?

As p-Value i.e. is less than Level of significance i.e (p-value:0.0331 < 0.05:Level of significance); Reject Null Hypothesis

Reject Ho. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,057.

d.

Repeat the preceding hypothesis test using the critical value approach.

a. Develop appropriate hypotheses such that rejection of Ho will support the researcher's contention.

b.

Ho :

Ha :

Sample size : Number of individuals who filed taxes return between April 10 and 15 : n = 400

sample mean refund : =  $910

Population Standard deviation of = $1,600

Hypothesized mean : = 1057

Test statistic = -1.84

For left tailed test :

Rejection rule

test statistic   Critical value -1.64

State your conclusion.

As Value of the test statistic is less than Critical Value i.e. ( -1.8375<-1.64 ); Reject Null Hypothesis

Reject Ho. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,057.