(a) The researcher might choose $0.01,0.05$, or 0.10 for the level of significance for the right-tailed test. For each potential choice for the level of significance, find the critical value. Round your answers to three decimal places. Critical value at $\alpha=0.01$ : $\square$ Critical value at $\alpha=0.05$ : $\square$ Critical value at $\alpha=0.10$ : $\square$ (b) After choosing the level of significance, the researcher takes a sample and finds that the value of the test statistic is $z=1.823$. For which of the levels of significance would the null hypothesis be rejected? Choose all that apply. $\alpha=0.01$ $\alpha=0.05$ $\alpha=0.10$ None of the above
Solution
Step 1 ：The problem is asking for the critical values at different levels of significance for a right-tailed test. The critical value is the value that the test statistic must exceed in order for us to reject the null hypothesis. In a right-tailed test, we reject the null hypothesis if the test statistic is greater than the critical value.
Step 2 ：The critical value can be found using the z-score table or a statistical software. The critical value is the z-score that corresponds to the given level of significance.
Step 3 ：The critical values for the given levels of significance are as follows: Critical value at \(\alpha=0.01\) : \(\boxed{2.326}\), Critical value at \(\alpha=0.05\) : \(\boxed{1.645}\), Critical value at \(\alpha=0.10\) : \(\boxed{1.282}\)
