Problem
Use the calculator displays to the right to make a decision to reject or fail to reject the null hypothesis at a significance level of $\alpha=0.05$. \begin{tabular}{|l|l|} \hline Z-Test & Z-Test \\ Inpt Data Stats $\mu \neq 80$ \\ $\mu_{0}: 80$ & $z=-2.47144355$ \\ $\sigma .4 .75$ & $p=0.01345688$ \\ $\times .78 .25$ & $\alpha=78.25$ \\ $n .45$ & $n=45$ \\ $\mu \neq \mu_{0}<\mu_{0}>\mu_{0}$ & \\ Calculate Draw & \\ \hline \end{tabular} Choose the correct answer below. A. Since the $P$-value is less than $\alpha$, fail to reject the null hypothesis. B. Since the $P$-value is greater than $\alpha$, reject the null hypothesis. C. Since the P-value is less than $\alpha$, reject the null hypothesis. D. Since the P-value is greater than $\alpha$, fall to reject the null hypothesis.
Solution
Step 1 ：The question is asking us to decide whether to reject or fail to reject the null hypothesis based on the P-value and the significance level \(\alpha\). The P-value is given as 0.01345688 and the significance level \(\alpha\) is given as 0.05.
Step 2 ：The rule of thumb is that if the P-value is less than or equal to the significance level, we reject the null hypothesis. If the P-value is greater than the significance level, we fail to reject the null hypothesis.
Step 3 ：In this case, the P-value is less than the significance level (0.01345688 < 0.05), so we should reject the null hypothesis.
Step 4 ：\(\boxed{\text{The correct answer is C. Since the P-value is less than } \alpha, \text{ reject the null hypothesis.}}\)
