Which of the following statements is not true a The reliabil

Which of the following statements is not true?

(a) The reliability of hypothesis testing procedure in reaching a correct decision can be assessed by studying type I error probability.

(b) The process of reaching a decision by using the methodology of classical hypothesis testing involves selecting a level of significance and then rejecting or not rejecting the null hypothesis H0 at that level .

(c) A small P-value would indicate statistical significance in that it would strongly suggest rejection H0 of in favor of Ha.

(d) A test with significance level is one for which the type I error probability is controlled at the specified level.

(e) A type I error is usually more serious than a type II error.

Solution

Statement \'a\' is incorrect.

Type I error = P(Rejecting the null hypothesis when it is true)

i.e we are rejecting our claim even though it is true. In other words we can say that we are minimising the losses which might occur due to a wrong decision.

As the type I error probability decreases, Type II error probability increases. By reducing the probability of type I error, we have reduced the losses which might occur to us due to the wrong decision but at the same time the probability of occurence of type II error has increased. Hence, we can conclude that by minimising the probability of type I error only the losses are minimised but it does not increases the reliability of hypothesis for taking a correct decision.