Question

In a test of statistical hypotheses, the p-value tells us__

o if the null hypothesis is true.
o if the alternative hypothesis is true.
o the largest level of significance at which the null hypothesis can be rejected.
o the smallest level of significance at which the null hypothesis can be rejected.

Answer 1

The p-value denotes the largest level of significance at which the null hypothesis can be rejected. A small p-value suggests strong evidence against the null hypothesis and leads to its rejection if it is below the preset significance level, usually 0.05.

Step-by-step explanation:

The p-value in a test of statistical hypotheses represents the probability that the observed data would occur if the null hypothesis were true. Specifically, it indicates the largest level of significance at which the null hypothesis can be rejected. This means that if the p-value is less than or equal to the significance level (commonly 0.05, or 5%), the null hypothesis is rejected in favor of the alternative hypothesis. Conversely, if the p-value is greater than the significance level, the null hypothesis is not rejected.

In hypothesis testing, a small p-value provides strong evidence against the null hypothesis, leading to its rejection. The p-value essentially quantifies the strength of the evidence against the null hypothesis. For example, a p-value of 0.01 suggests a stronger evidence against the null hypothesis than a p-value of 0.04, assuming the significance level is 0.05.