Question

In: Statistics and Probability

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,081....

Individuals filing federal income tax returns prior to March 31 received an average refund of $1,081. 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.

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 = $1800 may be assumed. What is the p-value (to 4 decimals)?

C. α = 0.05, what is the critical value for the test statistic? enter negative values as a negative number.

Solutions

Expert Solution

The provided sample mean is and the known population standard deviation is σ=1800, and the sample size is n=400.

A.

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=1081 i.e. individuals who wait until the last five days on average receive the same refunds as early filers.

Ha: μ<1081 i.e. individuals who wait until the last five days on average receive lower refunds as compared to early filers.

This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation, will be used.

B.

Test Statistics

The z-statistic is computed as follows:

The p-value is p = P(z<-1.9) = 0.0287

c.

Based on the information provided, the significance level is α=0.05, and the critical value for a left-tailed test is .

The rejection region for this left-tailed test is R={z:z<−1.64}

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orchestra answered 2 years ago
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