Consider the following statements concerning decision making using the hypothesis testing methodology: A. A Type II...

Consider the following statements concerning decision making using the hypothesis testing methodology:

A.     A Type II error cannot occur if the null hypothesis is rejected.
B.     Type I and II errors can occur simultaneously.
C.     A Type I error can occur if the null hypothesis is rejected.

which statement（s） is/are true？

Expert Solution

Statements A and C are True

___________________________________

(A) A Type II error is defined as the failure to reject a false null hypothesis. If the null hypothesis has been rejected, then it eliminates the possibility of a Type II error. In Such a case, either to reject the null was the correct decision or a Type I error has been made. Therefore this statement is TRUE.

(B) When doing Hypothesis testing, we either Reject the Null hypothesis or we fail to Reject the Null Hypothesis. Either the decision was correct in either case or we have made a Type I error by rejecting the null or made a Type II error by not rejecting the null. There is no event or outcome where both Type I and Type II errors can occur simultaneously.

Therefore this statement is FALSE.

(C) A Type I error is defined as the incorrect rejection of the null hypothesis. If we have rejected the null hypothesis, we have either made the correct decision or made a Type I error. Therefore this statement is TRUE.

orchestra answered 2 years ago

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