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)