Use the given information to find the $p$-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).
With $H_{1}: p \neq \frac{3}{5}$, the test statistic is $z=0.78$.
A. 0.4354 ; reject the null hypothesis
B. 0.2177 ; fail to reject the null hypothesis
c. 0.4354 ; fail to reject the null hypothesis
D. 0.2177 ; reject the null hypothesis
Answer
Final Answer: \(\boxed{C. 0.4354 ; fail to reject the null hypothesis}\)
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: \(\boxed{C. 0.4354 ; fail to reject the null hypothesis}\)
