According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. 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 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. 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. Test the researcher's assertion using the critical value approach. Use α = 0.05
According to the IRS, individuals filing federal income tax returns prior to March 31 received an average refund of $1056 in 2018. 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 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. 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.
Test the researcher's assertion using the critical value approach. Use α = 0.05
(Please include all the 7 steps in hypothesis testing)
Steps in hypothesis testing
p-value Approach
Develop the null and alternative hypothesis
Specify the level of significance, α
Choose the test statistic (z or t)
Calculate the test statistic
Use the value of the test statistic to compute the p-value.
Reject H0 if p-value ≤ α
Interpret the statistical conclusion in the context of the problem.
- Critical Value Approach
- Develop the null and alternative hypothesis
- Specify the level of significance, α
- Choose the test statistic (z or t)
- Use the level of significance to determine the critical value and the rejection rule
- Calculate the test statistic
- Compare test statistic to your rejection rule. Reject of Fail to Reject the null hypothesis
- Interpret the statistical conclusion in the context of the problem.
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