Question

Individuals filing federal income tax returns prior to March 31st received an

average refund of $1056. Consider the population of "last-minute" filers who mail

their tax return during the last five days of the income tax period.

1. A researcher suggest 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

Họ will support the researcher's contention.

2. For a sample of 400 individuals who filed a tax return last minute, the

sample mean refund was $910. Based on prior experience, a

population standard deviation of o = $1600 may be assumed. What is

the p-value?|

3. At a = 0.10, what is your conclusion?

Answer 1

1) NULL HYPOTHESIS H0: dollars

ALTERNATIVE HYPOTHESIS Ha: dollars

2) Test statistic under null hypothesis H0 is

Z= xbar-mean/sigma/sqrt(n)

Z= 910-1065/1600/sqrt(400)

Z= -155/1600/20

Z= -155/80

Z= 1.9375

Z= -1.94 (ROUND TO TWO DECIMALS)

The P-Value is .0262. The result is significant BECAUSE p < 0.1 (FROM P VALUE TABLE)

3) Conclusion: Since P value smaller than the level of significance therefore SIGNIFICANT. REJECT NULL HYPOTHESIS H0. WE HAVE SUFFICIENT EVIDENCE TO CONCLUDE THAT THE THESE INDIVIDUALS RECEIVE LOWER REFUNDS THAN DO EARLY FILLERS.