31 points
Part 1 of 3
Points: 0 of 1
Test the hypothesis using the P-value approach. Be sure to verify the requirements of the test.
\[
\begin{array}{l}
H_{0}: p=0.7 \text { versus } H_{1}: p> 0.7 \\
n=100 ; x=85 ; \alpha=0.05
\end{array}
\]

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Calculate the test statistic, $\mathrm{z}_{0}$.
\[
\mathrm{z}_{0}=\square
\]
(Round to two decimal places as needed.)

Step 1 ：Given that the sample proportion \(\hat{p} = \frac{x}{n} = \frac{85}{100} = 0.85\), the hypothesized population proportion \(p_0 = 0.7\), and the sample size \(n = 100\)

Step 2 ：We can calculate the test statistic for a hypothesis test for a proportion using the formula: \(z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1 - p_0)}{n}}}\)

Step 3 ：Substitute the given values into the formula: \(z = \frac{0.85 - 0.7}{\sqrt{\frac{0.7(1 - 0.7)}{100}}}\)

Step 4 ：Simplify the denominator: \(z = \frac{0.15}{\sqrt{0.0021}}\)

Step 5 ：Calculate the square root: \(z = \frac{0.15}{0.0458257569495584}\)

Step 6 ：Finally, calculate the value of z: \(z = 3.27\)

Step 7 ：So, the test statistic \(z_0\) is approximately \(\boxed{3.27}\) (rounded to two decimal places)