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

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.

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.

Test Statistics

The z-statistic is computed as follows:

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

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 1 year ago

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