Question 8 of 9
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Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
\[
\begin{array}{l}
H_{0}: p=0.3 \text { versus } H_{1}: p> 0.3 \\
n=100 ; x=35 ; \alpha=0.05
\end{array}
\]

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Calculate the test statistic, $\mathrm{z}_{0}$.
\[
\mathrm{z}_{0}=\square
\]
(Round to two decimal places as needed.)
Identify the P-value.
P-value $=\square$
(Round to three decimal places as needed.)
Choose the correct result of the hypothesis test for the P-value approach below.
A. Reject the null hypothesis, because the P-value is greater than $\alpha$.
B. Do not reject the null hypothesis, because the P-value is less than $\alpha$.
C. Do not reject the null hypothesis, because the P-value is greater than $\alpha$.
D. Reject the null hypothesis, because the P-value is less than $\alpha$.

Step 1 ：Calculate the test statistic, z0, using the formula: \(z0 = \frac{{\hat{p} - p0}}{{\sqrt{{p0 * (1 - p0) / n}}}}\)

Step 2 ：Substitute the given values into the formula: \(z0 = \frac{{0.35 - 0.3}}{{\sqrt{{0.3 * (1 - 0.3) / 100}}}}\)

Step 3 ：Simplify the equation to get: \(z0 = \frac{{0.05}}{{\sqrt{{0.21 / 100}}}}\)

Step 4 ：Further simplify to get: \(z0 = \frac{{0.05}}{{0.0458}}\)

Step 5 ：Round the result to two decimal places to get: \(z0 = 1.09\)

Step 6 ：Find the P-value, which is the probability of observing a test statistic as extreme as z0, given that the null hypothesis is true. Since this is a one-tailed test (H1: p > 0.3), find the area to the right of z0 = 1.09 on the standard normal distribution.

Step 7 ：Using a standard normal (Z) table or a calculator, find that the area to the left of z0 = 1.09 is approximately 0.8621. Therefore, the area to the right (which is the P-value) is 1 - 0.8621 = 0.1379 (rounded to four decimal places).

Step 8 ：Compare the P-value to the significance level, \(\alpha = 0.05\). If the P-value is less than \(\alpha\), reject the null hypothesis. If the P-value is greater than \(\alpha\), do not reject the null hypothesis.

Step 9 ：Since 0.1379 > 0.05, do not reject the null hypothesis. Therefore, the final answer is: \(\boxed{\text{Do not reject the null hypothesis, because the P-value is greater than } \alpha}\)