Step 1 :Given that the alternative hypothesis is \(H_{1}: p \neq \frac{3}{5}\), and the test statistic is \(z=0.78\).
Step 2 :This is a two-tailed test, so we need to find the area to the right of \(z=0.78\) and multiply it by 2 to get the p-value.
Step 3 :The calculated p-value is approximately 0.4354.
Step 4 :We compare the p-value with the significance level of 0.05. Since the p-value is greater than the significance level, we fail to reject the null hypothesis.
Step 5 :Final Answer: \(\boxed{C. 0.4354 ; fail to reject the null hypothesis}\)