Test the claim about the population mean, $\mu$, at the given level of significance using the given sample statistics.
Claim: $\mu=50 ; \alpha=0.06 ; \sigma=3.49$. Sample statistics: $\bar{x}=48.9, n=79$
The standardized test statistic is -2.80 .
(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.)
A. The critical value is
B. The critical values are \pm 1.88 .
Determine the outcome and conclusion of the test. Choose the correct answer below.
A. Reject $\mathrm{H}_{0}$. At the $6 \%$ significance level, there is enough evidence to support the claim.
B. Fail to reject $\mathrm{H}_{0}$. At the $6 \%$ significance level, there is not enough evidence to support the claim.
C. Fail to reject $\mathrm{H}_{0}$. At the $6 \%$ significance level, there is not enough evidence to reject the claim.
D. Reject $\mathrm{H}_{0}$. At the $6 \%$ significance level, there is enough evidence to reject the claim.
Answer
\(\boxed{\text{The critical values are } \pm 1.88. \text{ Reject } H_{0}. \text{ At the } 6\% \text{ significance level, there is enough evidence to reject the claim.}}\)
Step 1 ：Calculate the critical value using the Z-table for the given level of significance, which is 0.06. The critical values will be at the 0.03 and 0.97 quantiles since we are doing a two-tailed test. The critical value is approximately \(\pm 1.88\).
Step 2 ：Compare the critical value with the given test statistic (-2.80). If the absolute value of the test statistic is greater than the critical value, we reject the null hypothesis.
Step 3 ：The given test statistic is -2.80, which is less than -1.88. Therefore, we reject the null hypothesis.
Step 4 ：At the 6% significance level, there is enough evidence to reject the claim that the population mean is 50.
Step 5 ：\(\boxed{\text{The critical values are } \pm 1.88. \text{ Reject } H_{0}. \text{ At the } 6\% \text{ significance level, there is enough evidence to reject the claim.}}\)
