Which one is correct about hypothesis testing?

[songoku]

Homework Statement

Which one is valid about hypothesis testing?
a) The distribution of test statistic under the null hypothesis is the same as its distribution across experiments using random samples of the same size from the same population

b) The test statistic has same distribution when the null hypothesis is true and when alternative hypothesis is true

c) The null hypothesis is always more likely to be correct than alternative hypothesis

d) We use the distribution of the test statistic when null hypothesis is true

e) The distribution of test statistic under the null hypothesis depends on the direction of the extreme which comes from the alternative hypothesis

Relevant Equations

None

My attempt:

a) I am not really sure I understand this option fully but my answer will be this one is only applicable if the sample size is large and central limit theorem can be applied so (a) is wrong

b) The test statistic has "same distribution" to what? My opinion is (b) is wrong because distribution of test statistic is independent of whether null and alternative hypothesis are correct or not

c) I think this is correct because the probability of alternative hypothesis to be correct is the same as significance level used which is always lower than probability to accept null hypothesis

d) This is wrong because of the same reasoning as (b), distribution of test statistic is independent of whether null hypothesis is correct or not

e) This is wrong because distribution of test statistic is independent of alternative hypothesis


Am I correct? Thanks

 

[WWGD]

It may differ depending on the statistic you're testing for: mean, proportion, F-test for equality of Variance, etc.

 

[songoku]

It may differ depending on the statistic you're testing for: mean, proportion, F-test for equality of Variance, etc.

Oh I don't know about that.

Let say the context is hypothesis testing for difference in mean