Question

Suppose a hypothesis test is conducted using a significance or alpha level of 0.05, and the null hypothesis is rejected. This means that?

A we would also reject the null hypothesis if the significance level had been 0.10 instead of 0.05.

B the p-value was greater than 0.05.

C we would also reject the null hypothesis if the significance level had been 0.01 instead of 0.05.

D All answer options are correct.

Answer 1

We know that at 0.05 level of significance critical values are for a z test are -196 and +1.96.

Since we have rejected null hypothesis at 0.05 los it means value test Statistic must be greater than |1.96|

Critical values for 0.10 los is -1.64 and +1.64 since value of test Statistic was greater than |1.96| then it is obviously greater than |1.64|

It mean we would also reject the null hypothesis if the significance level had been 0.10 instead of 0.05

Option A is correct.

We reject null hypothesis if p value for test Statistic is less than the given alpha .

Option B is wrong because if p value was greater than alpha 0.05 we would not reject the null hypothesis.

Option C) we know that critical values for 0.01 level of significance is 2.58 since we had rejected the null hypothesis at 0.05 the test Statistic must must be greater than |1.96| and it does not confirm that test Statistic is greater than 2.58

Therefore option C is wrong

Option D) Since option B and C are wrong it means all option obviously are not correct.