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 \(\boxed{5.62}\).