Chapter 10, Problem AP3.16CPT

To determine

To find out form the following option that which of the following describes a Type II error.

Answer to Problem AP3.16CPT

Option (c) is the correct option.

Explanation of Solution

It is given in the question that:

  $\begin{array}{l}{H}_0:\mu =5\\ H_a:\mu >5\end{array}$

Now, Type II error is: Fail to reject the null hypothesis $H_0$ , when the null hypothesis $H_0$ is false.

Thus, we have to find out which of the following options describes a Type II error. As, we note that from Type II error, there is no convincing evidence that the true mean is greater than $5$ , when the true mean is actually greater than $5$ .

Therefore, we conclude that the correct option is (c) as this conclusion contains “fails to find convincing evidence” and also uses “do exceeds acceptable limits”. Thus, this statement best describes Type II error. Hence, option (c) is the correct option i.e. the EPA fails to find a convincing evidence that emissions exceed acceptable limits when they do actually exceed acceptable limits.