Question

test the hypothesis using the p - value approach. be sure to verify the requirements of the test
$h_0: p = 0.74$ versus $h_1: p \
eq 0.74$
$n = 500$, $x = 360$, $\alpha = 0.01$
(type an integer or a decimal. do not round)
a. yes, because $np_0(1 - p_0)=96.2$
b. no, because $np_0(1 - p_0)=$
now find $\hat{p}$.
$\hat{p}=0.72$ (type an integer or a decimal. do not round)
find the test statistic $z_0$
$z_0=-1.02$ (round to two decimal places as needed)
find the p - value
p - value $=0.308$ (round to three decimal places as needed)
state the conclusion of the hypothesis test.
because the p - value is than $\alpha$.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If the \(P - value\) is less than \(\alpha\), we reject \(H_0\). If the \(P - value\) is greater than \(\alpha\), we fail to reject \(H_0\).

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

We are given that \(P - value=0.308\) and \(\alpha = 0.01\). Since \(0.308>0.01\).

Answer:

Fail to reject \(H_0\) because the \(P - value\) is greater than \(\alpha\).