Question

A p-value that is smaller than α proves that the null hypothesis is false

a. The statement is false because a p-value that is smaller than α leads to the rejection of the null hypothesis, but it doesn't necessarily prove that the null hypothesis is false.
b. The statement is false because only p-values that are larger than α prove that the null hypothesis is false.
c. The statement is True

Answer 1

A p-value smaller than the significance level α does not prove the null hypothesis is false; it just indicates sufficient evidence to reject it in favor of the alternative hypothesis.

Step-by-step explanation:

The statement that a p-value smaller than α proves the null hypothesis is false is incorrect. Rather, a small p-value indicates strong evidence against the null hypothesis and typically leads to a decision to reject the null hypothesis. However, it does not provide proof that the null hypothesis is false, as statistical hypothesis testing is inherently probabilistic and does not deal with absolute certainties.

Therefore, the correct choice is: (a) The statement is false because a p-value that is smaller than α leads to the rejection of the null hypothesis, but it doesn't necessarily prove that the null hypothesis is false. To put it simply, if the p-value is low, the null must go; this does not mean it is proven false but rather that the evidence we have strongly suggests we should consider rejecting it in favor of the alternative hypothesis.