Question

test the claim about the population mean, \\( \mu \\), at the given level of significance using the given sample statistics.

claim: \\( \mu \
eq 6000 ; \alpha=0.09 ; \sigma=407 \\). sample statistics: \\( \bar{x}=6300, n = 38 \\)

identify the null and alternative hypotheses. choose the correct answer below.

\\( \bigcirc \\) a. \\( h_{0}: \mu \geq 6000 \\)
\\( h_{a}: \mu \
eq 6000 \\)
\\( \bigcirc \\) c. \\( h_{0}: \mu \leq 6000 \\)
\\( h_{a}: \mu \
eq 6000 \\)
\\( \bigcirc \\) e. \\( h_{0}: \mu \
eq 6000 \\)
\\( h_{a}: \mu \leq 6000 \\)
\\( \bigcirc \\) b. \\( h_{0}: \mu \
eq 6000 \\)
\\( h_{a}: \mu \geq 6000 \\)
\\( \bigcirc \\) d. \\( h_{0}: \mu \
eq 6000 \\)
\\( h_{a}: \mu=6000 \\)
\\( \bigcirc \\) f. \\( h_{0}: \mu=6000 \\)
\\( h_{a}: \mu \
eq 6000 \\)

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is a statement of equality or no difference. The alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. Here, the claim is \(\mu
eq6000\). The null hypothesis must be a statement of equality, so \(H_0:\mu = 6000\) and the alternative hypothesis \(H_a:\mu
eq6000\) (since the claim is about \(\mu\) not being equal to 6000).

Answer:

F. \(H_0:\mu = 6000\), \(H_a:\mu
eq6000\)