Question

given $h_0: mu geq 18$ and $p = 0.081$. do you reject or fail to reject $h_0$ at the $0.05$ level of significance?
a. reject $h_0$
b. not sufficient information to decide
c. fail to reject $h_0$

Explanation:

Step1: Recall the decision rule for hypothesis testing

If \(P - value<\alpha\) (level of significance), reject \(H_0\). If \(P - value\geq\alpha\), fail to reject \(H_0\).
Here, \(\alpha = 0.05\) and \(P=0.081\).

Step2: Compare \(P - value\) and \(\alpha\)

Since \(0.081>0.05\) (i.e., \(P - value>\alpha\)).

Answer:

C. fail to reject \(H_0\)