Question

AP3.25. Suppose the null and alternative hypotheses for a significance test are defined as $$\begin{gathered} H_0:\mu =40 \\ {H}_{\alpha }:\mu <40 \end{gathered}$$ Which of the following specific values for Ha will give the highest power?

(a) $\mu =38$

(b)$\mu =39$

(c) $\mu =42$

(d)$\mu =41$

(e)$\mu =42$

Short answer

$\mu =38$would give the highest power.

Hence ,the correct option is (a)

Step-by-step solution

Step 1. Given information

It is given that we have to suppose that the null and alternative hypothesis for a significance test are defined as

$$\begin{gathered} H_0:\mu =40 \\ {H}_{\alpha }:\mu <40 \end{gathered}$$

Step 2. Simplify

The smaller number of the value of $\mu$the easier it is reject the null hypothesis, therefore the solution would be the smallest number from the following options.

Hence ,the correct option is (a).