Choose the correct pair of hypotheses for this situation:
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} $H_{0}: p=0.368$ & $\begin{array}{l}H_{0}: p=0.368 \\ H_{a}: p \neq 0.368\end{array}$ & $\begin{array}{l}H_{0}: p=0.368 \\ H_{a}: p> 0.368 \\ H_{a}: p< 0.368\end{array}$ \\ \hline \end{tabular}
$(A) \quad(B)(C)(D)(E)(F)$
(B)
Using the normal approximation for the binomial distribution (without the continuity correction), was is the test statistic for this sample based on the sample proportion?
\[
z=
\]
(Report answer as a decimal accurate to 3 decimal places.)
You are now ready to calculate the P-value for this sample.
$P$-value $=$
(Report answer as a decimal accurate to 4 decimal places.)
Answer
The correct pair of hypotheses for this situation is \(\boxed{(B) \begin{array}{l}H_{0}: p=0.368 \\ H_{a}: p \neq 0.368\end{array}}\). We don't have enough information to calculate the test statistic or the P-value.
Step 1 ：The null hypothesis is typically a statement of no effect or no difference. The alternative hypothesis is what you might believe to be true or hope to prove true. In this case, the null hypothesis is given as \(H_{0}: p=0.368\). This means that we are assuming that the true population proportion is 0.368. The alternative hypothesis is a statement that contradicts the null hypothesis. It represents an effect or difference. There are three types of alternative hypotheses: \(H_{a}: p \neq 0.368\) (two-tailed test), \(H_{a}: p > 0.368\) (one-tailed test), \(H_{a}: p < 0.368\) (one-tailed test). The correct pair of hypotheses would be one null hypothesis and one alternative hypothesis. Therefore, the correct answer is \(H_{0}: p=0.368\) and \(H_{a}: p \neq 0.368\).
Step 2 ：The second part of the question is asking for the test statistic for this sample based on the sample proportion. However, we don't have enough information to calculate this. We would need the sample proportion and the sample size to calculate the test statistic.
Step 3 ：The third part of the question is asking for the P-value for this sample. Again, we don't have enough information to calculate this. We would need the test statistic and the type of test (one-tailed or two-tailed) to calculate the P-value.
Step 4 ：The correct pair of hypotheses for this situation is \(\boxed{(B) \begin{array}{l}H_{0}: p=0.368 \\ H_{a}: p \neq 0.368\end{array}}\). We don't have enough information to calculate the test statistic or the P-value.
