In testing the hypotheses: $H _ { 0 } : p = 0.50$ $H _ { 1 } : p \neq 0.50$ , at the 10% significance level, if the sample proportion is 0.56, and the standard error of the sample proportion is 0.025, the appropriate conclusion is:
A) to reject $\mathcal { H } _ { 0 }$ .
B) not to reject $\mathcal { H } _ { 0 }$ .
C) to reject $H _ { 1 }$ .
D) to reject both $\mathcal { H } _ { 0 }$ and $H _ { 1 }$ .

Question

Quizplus · Accepted Answer

Using the formula for the z-test, we can calculate the test statistic:
$$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.56-0.50}{0.025}=2.4$$
Since this is a two-tailed test, the critical value for a 10% significance level is approximately 1.645. Since the test statistic is greater than the critical value, we reject the null hypothesis. Therefore, the appropriate conclusion is to reject $H _ { 0 }$.

In Testing the Hypotheses H0:p=0.50H _ { 0 } : p = 0.50H0​:p=0.50

In Testing the Hypotheses $H _ { 0 } : p = 0.50$