Question

Consider the following statements. (i) The p-value is calculated under the assumption that the alternative hypothesis is true. (ii) The smaller the p-value, the stronger the evidence is in favor of the null hypothesis. (iii) The p-value forms the borderline between values of the test statistic that would result in rejecting the null hypothesis and values of the test statistic that would result in not rejecting the null hypothesis. Determine which of the above statements are true (1) or false (2).

Answer 1

(i). False, the p-value is calculated under the assumption that the null hypothesis is true. P-value is the probability of the test statistic and the parameters if null hypothesis is true. Greater the p-value, greater the evidence to support the null hypothesis.

(ii). The smaller the p-value, the lesser the evidence in support of null hypothesis. As we know, for a 95% C.I., we reject null hypothesis if p-value < 0.05. Or, there is only less than 5% chance in favour of null hypothesis due to which it is taken as the contribution of error and not any considerable factor's influence.

(iii). The p-value is minimum value level of significance can take, below the value of , the null hypothesis is rejected as here corresponding test statistic belong to the rejection region and above the value of is the acceptance region where corresponding test statistic leads to the acceptance of null hypothesis.