Question

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 \leq 1160 ; \alpha=0.08 ; \sigma=199.88 \\). sample statistics: \\( \bar{x}=1185.66, n=200 \\)

\\( \bigcirc \\) a. \\( h_{0}: \mu \geq 1160 \\)
\\( h_{a}: \mu<1160 \\)
\\( \bigcirc \\) b. \\( h_{0}: \mu>1160 \\)
\\( h_{a}: \mu \leq 1160 \\)
\\( \bigcirc \\) c. \\( h_{0}: \mu \geq 1185.66 \\)
\\( h_{a}: \mu<1185.66 \\)
\\( \bigcirc \\) d. \\( h_{0}: \mu \leq 1185.66 \\)
\\( h_{a}: \mu>1185.66 \\)
\\( \bigcirc \\) e. \\( h_{0}: \mu>1185.66 \\)
\\( h_{a}: \mu \leq 1185.66 \\)
\\( \bigcirc \\) f. \\( h_{0}: \mu \leq 1160 \\)
\\( h_{a}: \mu>1160 \\)

calculate the standardized test statistic.

the standardized test statistic is 1.82
(round to two decimal places as needed.)

determine the p - value.

\\( p=0.034 \\) (round to three decimal places as needed.)

determine the outcome and conclusion of the test.

\\( h_{0} \\). at the \\( 8 \\% \\) significance level, there enough evidence to the claim.

Explanation:

Step1: Hypothesis testing rule

In hypothesis testing, if the \(P - value\leq\alpha\), we reject \(H_{0}\). Here, \(\alpha = 0.08\) and \(P=0.034\).

Step2: Compare \(P - value\) and \(\alpha\)

Since \(0.034<0.08\) (i.e., \(P - value<\alpha\)).

Answer:

Reject \(H_{0}\). At the \(8\%\) significance level, there is enough evidence to reject the claim.