Consider the following hypothesis,
\[
\begin{array}{l}
H_{0}: p=0.7 \quad \mathrm{x}=178, \mathrm{n}=202 \\
H_{a}: p \neq 0.7
\end{array}
\]

Find the test statistic (Step 2)

Round your answer to two decimal places.

Step 1 ：Consider the following hypothesis, \(H_{0}: p=0.7\) where \(x=178, n=202\) and \(H_{a}: p \neq 0.7\).

Step 2 ：Calculate the sample proportion, \(p_{hat} = \frac{x}{n}\).

Step 3 ：Substitute the given values into the formula, \(p_{hat} = \frac{178}{202} = 0.8811881188118812\).

Step 4 ：Calculate the test statistic, \(Z = \frac{p_{hat} - p_0}{\sqrt{(p_0 * (1 - p_0)) / n}}\).

Step 5 ：Substitute the given values into the formula, \(Z = \frac{0.8811881188118812 - 0.7}{\sqrt{(0.7 * (1 - 0.7)) / 202}} = 5.62\).

Step 6 ：Round the test statistic to two decimal places, \(Z = 5.62\).

Step 7 ：The final answer is \(\boxed{5.62}\).