Question

According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1,090 in 2018 . Consider the population of "last-minute" filers who mail their tax return during the last five days of the income tax period (typicall 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 Hwill support the researcher's contention. H:μ is 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 p-value (to 4 decimals)? c. Using α=0.05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? d. Repeat the preceding hypothesis test using the critical value approach. Using α=0.05, what is the critical value for the test statistic (to 3 decimals)? Enter negative value as negative number. State the rejection rule: Reject H

Answer 1

The researcher suggests that individuals who wait until the last five days to file their tax returns receive lower refunds than early filers. The p-value is 0.0122, indicating that there is enough evidence to support the researcher's contention. With a significance level of 0.05, we can conclude that the population mean refund for last-minute filers is indeed less than the population mean refund for early filers. The critical value for the test statistic is -1.645.

Step-by-step explanation:

a. Hypotheses:

H0: μ ≥ $1,090 (Mean refund for last-minute filers is greater than or equal to the mean refund for early filers)

HA: μ < $1,090 (Mean refund for last-minute filers is less than the mean refund for early filers)

b. P-value:

Z = (X − μ) / (σ / sqrt(n))

Z = (910 − 1090) / (1600 / sqrt(400)) = -2.25

P-value = P(Z < -2.25) = 0.0122 (to 4 decimals)

c. Conclusion:

Since the p-value (0.0122) is less than the significance level (0.05), we can reject the null hypothesis. There is enough evidence to conclude that the population mean refund for last-minute filers is less than the population mean refund for early filers.

d. Critical Value:

Since α is 0.05 and it's a one-tailed test, the critical value for the test statistic is -1.645 (to 3 decimals).

Rejection Rule:

If the test statistic is less than -1.645, we reject the null hypothesis.