Question

A hypothesis test using a significance level of

= 0.05
produces a P-value of 0.066.
Which of the following conclusions is appropriate?
Accept the null (WHICH WE NEVER DO!) hypothesis at = 0.05 level.
Do not reject the null hypothesis at = 0.05 level.
Reject the null hypothesis at = 0.05 level.
Reject the alternative hypothesis at = 0.05 level.

Answer 1

The conclusion for a hypothesis test with a P-value of 0.066 and a significance level of 0.05 is to not reject the null hypothesis, indicating insufficient evidence against it.

Step-by-step explanation:

Given the scenario where a hypothesis test produces a P-value of 0.066 and the significance level (alpha) is 0.05, the appropriate conclusion would be 'Do not reject the null hypothesis at alpha = 0.05 level.' When comparing the P-value with the significance level, if the P-value is greater than alpha, we do not have sufficient evidence to reject the null hypothesis. In the provided case, since the P-value (0.066) is greater than the significance level (0.05), we conclude that there is not enough evidence to support the alternative hypothesis.

In summary, at the 5 percent significance level, there is insufficient evidence to conclude that the null hypothesis is false. Therefore, we do not reject the null hypothesis based on the available data.

Answer 2

Do not reject the null hypothesis at = 0.05 level.

Step-by-step explanation:

There's a saying like " If P is low, H.o must go" or "if P is low, reject the H.o".

H.o is another way of saying null hypothesis.

In our situation, our p values is actually bigger than the significance level thus we cannot reject the H0. We can never accept accept null. Thus the only thing we can say is "Do not reject the null hypothesis at = 0.05 level". We also say "Fail to reject the null".

I don't know about what you were taught but for me, we were taught to usually not bring alternative hypothesis in discussion b/c the point of the whole study is to disprove or find contrary information to null hypothesis thus we either reject null or fail to reject it (nothing to do with alternate)