Question

You may need to use the appropriate appendix table or technology to answer this question. Individuals filing federal income tax returns prior to March 31 received an average refund of $1,063. 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 Ho will support the researcher's contention. O Ho: u 2 $1,063 H: < $1,063 O Hou s $1,063 Hu> $1,063 O Hou < $1,063 Hau 2 $1,063 O Ho: u = $1,063 Hau$1,063 O Hoiu > $1,063 Haus $1,063 (b) For a sample of 400 individuals who filed tax return between April 10 and 15, the sample mean refund was $910. Based on prior experience, a population standard deviation of o = $1,600 may be assumed. What is the test statistic? (Round your answer to two decimal places.) What is the p-value? (Round your answer to four decimal places.) p-value = (c) At a = 0.05, what is your conclusion? O Do not reject Ho. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,063. Reject Ho. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less than or equal $1,063. Reject Ho. There is sufficient evidence to conclude that the mean refund of "last minute" filers is less than $1,063. Do not reject Ho. There is insufficient evidence to conclude that the mean refund of "last minute" filers is less or equal than $1,063.

Answer 1

Let ll be the average refund = $1,063 a) Hypothesis Ho: U = $1,063 Ha el 3 $1,063 b) Sample size, n=400 Sample mean refund, t = $910 Population Standard deviation, 0 = $1,600 Test statistic z = X-el own 910-1,063 (l 16001400 -IS3 80 -1.91 P-value - 0,0280 p-rauce, -1.91 c) At a = 0,05 P-value < a Hence reject. Ho Conclusion ! Reject Ho. There is sufficient evidence to conclude that the mean refund of ' last minute filers is less than $ 1,063.

Hie: ܙ d) Hypothesis el = $1,063 Ha u < $1.063 Test statistic Z - -1.91 At a = 0,05 the critical valueis, - Za =-Zo.os =-1.64 Rejection region is, test statistic < -1.64 :: Z C-Za Hence reject Ho conclusion '. Rejest Ho. There is sufficient evidence to conclude that the mean refund of last minute filers is less than $1,063