Question

In an independent sample sample t test, the researcher rejects H0 at 5% level of significance and fails to reject H0 at 1% level. Then the p-value of the test is

a.
more than 0.05

b.
less than 0,01

c.
0.01 < p < 0.05

d.
Cannot determine from given information.

Answer 1

Note that we fail to reject the null hypothesis when the p value is greater than significance level (alpha). If p value is less than significance level then we will reject the null hypothesis and accept the alternative hypothesis.

Here, the researcher rejects H0 at 5% level of significance, so we can say that p value is less than 0.05 (5%).

It is also given that the researcher fails to reject H0 at 1% level, so we can say that in this case p value is greater than 0.01 (1%).

So, p value is greater than 0.01 but less than 0.05.

i.e. option c. 0.01 < p < 0.05 is the correct answer.