Help with stats problem!!!

[NoSpoon]

So my stats teacher and I have a disagreement. The following was a homework question and the two relevant multiple choice answers:


If a null hypothesis was rejected at a significance level of 0.05, then:

A. We would have rejected the null hypothesis at the sig. level of 0.01 but not necessarily at sig. level of 0.1.

D. We would have rejected the null hypothesis at the sig. level of 0.1 but not necessarily at sig. level of 0.01.


I know why he picked the answer that he did, but I believe it should be the opposite. What do people think the correct answer should be and why? I'm not going to put which answer I think is correct to avoid biases.

Thanks!

[Practicing]

A.

Significance level refers to the probability that the sample data was selected given that the null hypothesis is correct. When rejecting the null hypothesis at a significance level of .05, we are stating that if the probability of our specific sample data being selected is less than .05 given our null hypothesis, we will reject the null. This statement includes the level of .01 but not necessarily the level of .1.

[Eric61483]

D.

P value, not level of significance, refers to the probability that the sample data was selected given that the null hypothesis is correct. The null hypothesis is rejected when P < level of significance. If null hypothesis is rejected at 0.05, then P < 0.05. It follows then that P < 0.1, so the null hypothesis is rejected at 0.1. We are not sure how P compares to 0.01, though.

[clarinetist]

Let P be the given P value. If a null hypothesis is rejected at , then . Since , , which means that if , the null hypothesis will be rejected. However, we cannot guarantee that . The answer must therefore be D.

[NoSpoon]

I agree with D, but my teacher kept arguing A. I think maybe the wording is a little ambiguous...

[Eric61483]

I do not see how the wording is ambiguous, assuming significance level = level of significance, which certainly would have been defined in the course.

[Baby, ByeBye]

D. Your teacher is a terd. Change schools.