Question

It has been reported that among those who file their income tax returns , the mean amou of tax refund is $ 1056 , with a standard deviation of s=$1400 . A study was done to determine whether people who file their tax return during the last 5 days before the deadline get a smaller refund , on average , than that of the entire population . A random sample of 64 "last minute " filers was taken and the average refund was calculated to be $640 . Which of the following statements is true ?
A. We cannot reject H 0 at the 10 % level of significance
B. We can reject H 0 at the 5% , but not the 1% level of significance
C. We can reject H 0 at the 1% , but not at the 0.1 % level of significance
D. We can reject H 0 at the 10 % , but not the 5% level of significance
E. We can reject H 0 at the 0.1 % level of significance

Answer 1

To Test :-

H0 :- µ = 1056
H1 :- µ < 1056

Test Statistic :-
Z = ( X - µ ) / ( σ / √(n))
Z = ( 640 - 1056 ) / ( 1400 / √( 64 ))
Z = -2.3771

α = 5%

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.05) = 1.645
Z < -Z(α) = -2.3771 < -1.645
Result :- Reject null hypothesis

α = 10%

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.1) = 1.282
Z < -Z(α) = -2.3771 < -1.282
Result :- Reject null hypothesis

α = 1%

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.01) = 2.326
Z < -Z(α) = -2.3771 < -2.326
Result :- Reject null hypothesis

α = 0.1%

Test Criteria :-
Reject null hypothesis if Z < -Z(α)
Critical value Z(α) = Z(0.001) = 3.09
Z > -Z(α) = -2.3771 > -3.09
Result :- Fail to reject null hypothesis

True statements are

C. We can reject H 0 at the 1% , but not at the 0.1 % level of significance