Question

A sample has a mean of M = 60 and a t statistic of t = 4.5. For a one-tailed hypothesis test with α = .01, what is the correct statistical decision for this sample? Why?

a.	The researcher can reject the null hypothesis with α = .05 but not with α = .01.
b.	The researcher can reject the null hypothesis with either α = .05 or α = .01.
c.	The researcher must fail to reject the null hypothesis with either α = .05 or α = .01.
d.	It is impossible to make a decision about H0 without more information.

Why?

Answer 1

The correct option is Option d: It is impossible make a decision about H0 without more information.

This is because this is a t test and the critical value of the t test depends on the degrees of freedom. If the sample size was 3 , then critical values of = 0.01 would be greater than 4.5 and the critical value for = 0.05 would be less than 4.5. In this at = 0.01, we would fail to reject H0, whereas at = 0.05 we would reject H0.

If the sample size was 30 then the critical values for = 0.01 and = 0.05, would both be less than 4.5, in which case, H0 would be rejected for both.

Since 2 different possibilities arise, we cannot make a decision about H0 without more information.