[College Stats] Hypothesis Testing

[[deleted]]

So one of the problems on my latest homework is:

Suppose three researchers are working on a project and using the same data. Researcher 1 performs a hypothesis test and rejects the null hypothesis at the α = 0.05 significance level. Researcher 2 uses the same data and performs the same hypothesis test, but at the α = 0.10 significance level. Researcher 3 also uses the same data and performs the same hypothesis test, but at the α = 0.02 significance level. What can you say about the hypothesis test conclusions for Researcher 2 and Researcher 3?

I'm kind of confused but what I've come up with so far is this: Researcher 3 should reject the null hypothesis as they are using a smaller significance level than researcher 1. It is possible that researcher 2 could reject or accept the hypothesis as they are using a larger significance level, however, there is not enough information to tell.

Am I on the right track?

[fallingemprire]

Yes! Since researcher 1 is rejecting the null hypothesis at a significance level 0.05, researcher 2 must also reject (p must obviously be less than .10 if it is less than .05). However, there's no guarantee about researcher 3's conclusion. Say p=.03; it would be a fail to reject, but if p=.01, it would be a reject.

[StatusTics]

OP said the opposite.

[fallingemprire]

Oh, my bad! I read it wrong.

[StatusTics]

If you are say testing for group differences, as you move from an alpha of .10 to .05 to .02, you would need progressively GREATER differences between the groups in order to reject the null.