Question

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 $1,052. 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. H0: μ > $1,052 Ha: μ ≤ $1,052 H0: μ = $1,052 Ha: μ ≠ $1,052 H0: μ < $1,052 Ha: μ ≥ $1,052 H0: μ ≥ $1,052 Ha: μ < $1,052 H0: μ ≤ $1,052 Ha: μ > $1,052 (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.) p-value = (c) At α = 0.05, what is your conclusion? Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,052. Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,052. Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,052. Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,052. (d) Repeat the preceding hypothesis test using the critical value approach. State the null and alternative hypotheses. H0: μ > $1,052 Ha: μ ≤ $1,052 H0: μ = $1,052 Ha: μ ≠ $1,052 H0: μ < $1,052 Ha: μ ≥ $1,052 H0: μ ≥ $1,052 Ha: μ < $1,052 H0: μ ≤ $1,052 Ha: μ > $1,052 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. Do not reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,052. Do not reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,052. Reject H0. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,052. Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,052.

Answer 1

a) The test hypothesis is :

H0: μ ≥ $1,052 Ha: μ < $1,052

b) The test statistic is given by:

. the above test statistic follows standard normal under the null hypothesis. thus the p-value = p(Z<-1.78) = 0.0379

c) The p-value is less than the significance level: Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,052.

d) The test hypothesis is :

H0: μ ≥ $1,052 Ha: μ < $1,052

The test statistic is given by:

.

the critical value for the test statistic  ≤ -1.645, test statistic ≥ None.

Conclusion: Reject H0. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,052.