Use technology to help you test the claim about the population mean, $\mu$, at the given level of significance, $\alpha$, using the given sample statistics. Assume the population is normally distributed.
Claim: $\mu> 1240 ; \alpha=0.06 ; \sigma=203.01$. Sample statistics: $\bar{x}=1265.45, n=275$
Identify the null and alternative hypotheses. Choose the correct answer below.
A.
\[
\begin{array}{l}
H_{0}: \mu> 1240 \\
H_{a}: \mu \leq 1240
\end{array}
\]
C.
\[
\begin{array}{l}
H_{0}: \mu \leq 1265.45 \\
H_{a}: \mu> 1265.45
\end{array}
\]
E.
\[
\begin{array}{l}
H_{0}: \mu> 1265.45 \\
H_{a}: \mu \leq 1265.45
\end{array}
\]
B.
\[
\begin{array}{l}
H_{0}: \mu \leq 1240 \\
H_{a}: \mu> 1240
\end{array}
\]
D.
\[
\begin{array}{l}
H_{0}: \mu \geq 1240 \\
H_{a}: \mu< 1240
\end{array}
\]
F.
\[
\begin{array}{l}
H_{0}: \mu \geq 1265.45 \\
H_{a}: \mu< 1265.45
\end{array}
\]
Answer
Final Answer: \(\boxed{H_{0}: \mu \leq 1240 , H_{a}: \mu>1240}\)
Step 1 ：Identify the null and alternative hypotheses. The null hypothesis (H0) is a statement of no effect or no difference and is the assumption that any kind of difference or significance you see in a set of data is due to chance. The alternative hypothesis (Ha) is a statement which we will accept if we find the null hypothesis to be unlikely.
Step 2 ：Given the claim is that the population mean, μ, is greater than 1240, the null hypothesis should be the opposite of the claim. Therefore, the null hypothesis should be that the population mean is less than or equal to 1240. The alternative hypothesis should be the claim itself, that the population mean is greater than 1240.
Step 3 ：So, the correct answer should be: \(H_{0}: \mu \leq 1240 \) and \(H_{a}: \mu>1240\)
Step 4 ：Final Answer: \(\boxed{H_{0}: \mu \leq 1240 , H_{a}: \mu>1240}\)
