Chapter 10, Problem AP3.25CPT

To determine

To find out which of the following specific values in the options for $H_a$ will give the highest power.

Answer to Problem AP3.25CPT

Option (a) is the correct option.

Explanation of Solution

It is given that:

  $\begin{array}{l}{H}_0:\mu =40\\ H_a:\mu <40\end{array}$

We have to calculate the highest power that $H_a$ will take. So, as we know that the true value of $\mu$ was actually not $40$ but less than the number $40$ . Thus, let us assume that $\mu =-10$ then the data to be centered around $-10$ and that almost any dataset generated we have rejected the null hypothesis and thus conclude that the value of $\mu \le 40$ . Therefore, the smaller the value of $\mu$ it is easier to reject the null hypothesis.

Thus it has to be near to the value $40$ . Therefore, the value of $\mu =38$ . Thus, option (a) is the correct option.