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 :\(\boxed{\text{The critical values are } \pm 1.88. \text{ Reject } H_{0}. \text{ At the } 6\% \text{ significance level, there is enough evidence to reject the claim.}}\)