Question

find the p - value for a left - tailed hypothesis test with a test statistic of ( z=-1.08 ). decide whether to reject ( h_{0} ) if the level of significance is ( alpha = 0.05 ).
p - value ( = 0.1401 ) (round to four decimal places as needed.)
state your conclusion. choose the correct answer below.
( \bigcirc ) since ( pleqalpha ), fail to reject ( h_{0} ).
( \bigcirc ) since ( p>alpha ), fail to reject ( h_{0} ).
( \bigcirc ) since ( p>alpha ), reject ( h_{0} ).
( \bigcirc ) since ( pleqalpha ), reject ( h_{0} ).

Explanation:

Step1: Recall the decision rule for hypothesis testing

In hypothesis testing, if \(P - value\leq\alpha\), we reject \(H_0\). If \(P - value>\alpha\), we fail to reject \(H_0\). Here, the \(P - value = 0.1401\) and \(\alpha=0.05\).

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

Since \(0.1401>0.05\) (i.e., \(P - value>\alpha\)).

Answer:

Since \(P>\alpha\), fail to reject \(H_0\). So the correct answer is: Since \(P > \alpha\), fail to reject \(H_0\).