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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. H 0: μ is Selectgreater than or equal to 1,081greater than 1,081less than or equal to 1,081less than 1,081equal to 1,081not equal to 1,081 H a: μ is Selectgreater than or equal to 1,081greater than 1,081less than or equal to 1,081less than 1,081equal to 1,081not equal to 1,081 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 = $1,800 may be assumed. What is the p-value (to 4 decimals)? c. Using α = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers? SelectYesNo Answer the next three questions using the critical value approach. d. Using α = .05, what is the critical value for the test statistic? e. State the rejection rule: Reject H 0 if z is Selectgreater than or equal togreater thanless than or equal toless thanequal tonot equal to the critical value. f. Using α = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? SelectYesNo

Solutions

Expert Solution

b.

The p-value is 0.0287

c.

Since p-value is less than α = .05, you can conclude that the population mean refund for "last minute" filers is less than the population mean refund for early fliers. Yes

d. Using α = .05, what is the critical value for the test statistic?

critical value = -1.96

e. State the rejection rule:

Reject H 0 if z is < = -1.96, reject H0

. f. Using α = .05, can you conclude that the population mean refund for "last minute" filers is less than the population mean refund for early filers? Yes

orchestra answered 2 years ago
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