Question

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

Explanation:

Step1: Recall hypothesis testing critical regions

In hypothesis testing, a one - sided (left - tailed in this case) critical region corresponds to a specific alternative hypothesis.

Step2: Analyze each alternative hypothesis

• For \(H_1:\mu = k\), it is a null - like statement (not an alternative in the context of critical regions for testing).
• For \(H_1:\mu>k\), the critical region would be on the right - side of the distribution.
• For \(H_1:\mu

eq k\), the critical region is two - tailed (both left and right sides).

• For \(H_1:\mu < k\), the critical region is on the left - side of the distribution as shown in the figure.

Answer:

\(H_1:\mu < k\)