Question

Suppose the null and alternative hypotheses for a significance test are defined as

$$\begin{gathered} {\mathrm{H}}_0:\mu =40 \\ {H}_a:\mu <40 \end{gathered}$$

Which of the following specific values for $H_a$will give the highest power?

(a) role="math" localid="1653066322242" $\mu =38$

(b) $\mu =40$

(c) $\mu =42$

(d) $\mu =41$

Short answer

The Specific values for$H_a$is$\mu =38$.

Step-by-step solution

Given Information

Given in the question that,

$$\begin{gathered} {\mathrm{H}}_0:\mu =40 \\ {H}_a:\mu <40 \end{gathered}$$

Explanation 

The smaller the value of $\mu$, the easier it is to reject the null hypothesis, hence the smallest integer from the following possibilities would be the solution.

As a result, the best solution is (a)