Question

multiple choice 4 points
select the most appropriate response.
which type of alternative hypothesis would have the critical region shown in the figure below?
$h_1:mu = k$
$h_1:mu > k$
$h_1:mu < k$
$h_1:mu
eq k$

Explanation:

Step1: Analyze one - tailed and two - tailed tests

A two - tailed test \(H_1:\mu
eq k\) has critical regions in both tails. A one - tailed test \(H_1:\mu > k\) has the critical region in the right - tail, and \(H_1:\mu < k\) has the critical region in the left - tail.

Step2: Match the critical region

The given critical region is in the left - tail. So, it corresponds to the alternative hypothesis \(H_1:\mu < k\).

Answer:

\(H_1:\mu < k\)