4. Individuals filing federal income tax returns prior to March 31 had an averag

Question

4. Individuals filing federal income tax returns prior to March 31 had an average refund of $1102. Consider the population of "last-minute" filers who mail their returns during the last five days of the income tax period (typically April 10 to April 15). a. A researcher suggests that one of the reasons that individuals wait until the last five days to file their returns is that on average those individuals have a lower refund than early filers. Develop appropriate hypotheses such that rejection of Ho will support the researcher's contention. b. For a sample of 600 individuals who filed a return between April 10 and April 15, the sample mean refund was $1050 and the standard deviation was $500. Compute the p-value. c. Using a .05, what is your conclusion? d. Test the hypotheses using the critical value approach (a 0,025)

Explanation / Answer

Q4.
Given that,
population mean(u)=1102
sample mean, x =1050
standard deviation, s =500
number (n)=600
null, Ho: =1102
alternate, H1: <1102
level of significance, = 0.05
from standard normal table,left tailed t /2 =1.647
since our test is left-tailed
reject Ho, if to < -1.647
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =1050-1102/(500/sqrt(600))
to =-2.547
| to | =2.547
critical value
the value of |t | with n-1 = 599 d.f is 1.647
we got |to| =2.547 & | t | =1.647
make decision
hence value of | to | > | t | and here we reject Ho
p-value :left tail - Ha : ( p < -2.5475 ) = 0.00555
hence value of p0.05 > 0.00555,here we reject Ho

ANSWERS
---------------
null, Ho: =1102
alternate, H1: <1102
test statistic: -2.547
critical value: -1.647
decision: reject Ho
p-value: 0.00555

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