What is significance good for? Which of the following questions does a significance test answer? Justify your answer.

(a) Is the sample or experiment properly designed?

(b) Is the observed effect due to chance?

(c) Is the observed effect important?

We have to fin out that Is the sample or experiment properly designed.

A significance test tests the claim made. It investigates the claim by forming the null hypothesis and alternate hypothesis. It accepts or rejects the hypothesis on the basis of $p$- value. It cannot check whether the sample or the experiment is properly designed or not.

We have to find out Is the observed effect due to chance.

Yes, the significance test finds that the observed effect is due to chance. The significance test measures the observed difference between the group using the $p$-value. The observed effect is due to chance only if the observed effect has a value more than calculated value at the given significance level.

If the$p-value<\alpha$, accept the null hypothesis.

If the $p-value\ge \alpha$reject null hypothesis.

In the second case, observed effect has a value more than calculated value.

We have to find out that Is the observed effect important.

A significance test tests the claim made. It cannot tell if the observed effect is important or not. It can only test the claim on the basis of $p$-value and cannot check if the observed effect is important.