Question

test the claim about the population mean, μ, at the given level of significance using the given sample statistics. claim: μ≠6000; α = 0.09; σ = 407. sample statistics: (\bar{x}=6300), n = 38 (h_{a}:mu
eq6000) (h_{a}:mu = 6000) oe. (h_{0}:mu
eq6000) (h_{a}:muleq6000) f. (h_{0}:mu = 6000) (h_{a}:mu
eq6000) calculate the standardized test statistic. the standardized test statistic is 4.54. (round to two decimal places as needed.) determine the critical value(s). select the correct choice below and fill in the answer box to complete your choice. (round to two decimal places as needed.) oa. the critical value is ob. the critical values are ±1.70. determine the outcome and conclusion of the test. choose from the following. oa. reject (h_{0}). at the 9% significance level, there is enough evidence to support the claim. ob. fail to reject (h_{0}). at the 9% significance level, there is not enough evidence to reject the claim. oc. reject (h_{0}). at the 9% significance level, there is enough evidence to reject the claim. od. fail to reject (h_{0}). at the 9% significance level, there is not enough evidence to support the claim.

Explanation:

Step1: Recall the decision rule for hypothesis testing

If the standardized test statistic \( z \) is in the rejection region (i.e., \( |z|>z_{\alpha/2} \)), we reject the null hypothesis \( H_0 \). Here, \( z = 4.54 \) and \( z_{\alpha/2}=1.70 \) (since it is a two - tailed test with \( \alpha = 0.09 \), so \( \alpha/2=0.045 \) and from the standard normal table \( z_{0.045}\approx1.70 \)).

Step2: Compare the test statistic and the critical value

Since \( |4.54| = 4.54>1.70 \), the test statistic falls in the rejection region.

Answer:

A. Reject \( H_0 \). At the \( 9\% \) significance level, there is enough evidence to support the claim.