Complete parts (a) through (c) below. (a) Determine the critical value(s) for a right-tailed test of a population mean at the $\alpha=0.10$ level of significance with 10 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the $\alpha=0.01$ level of significance based on a sample size of $n=15$. (c) Determine the critical value(s) for a two-tailed test of a population mean at the $\alpha=0.10$ level of significance based on a sample size of $n=11$. Click here to view the t-Distribution Area in Right Tail. (a) $t_{\text {crit }}=+1.372$ (Round to three decimal places as needed.) (b) $t_{\text {crit }}=\square \square$ (Round to three decimal places as needed.)

Step 1 ：The critical value is the point (or points) on the scale of the test statistic beyond which we reject the null hypothesis, and, is derived from the level of significance α of the test.

Step 2 ：For a right-tailed test, the critical value is the value such that the area to its right under the curve is equal to α. For a left-tailed test, the critical value is the value such that the area to its left under the curve is equal to α. For a two-tailed test, the critical values are the values such that the area to their left and right under the curve is equal to α/2.

Step 3 ：For part (a), the critical value for a right-tailed test at the α=0.10 level of significance with 10 degrees of freedom is \(t_{\text {crit }}=+1.372\).

Step 4 ：For part (b), we need to find the critical value for a left-tailed test with α=0.01 and n=15. The degrees of freedom is n-1=14. The critical value is \(t_{\text {crit }}=\boxed{-2.624}\) (rounded to three decimal places).

Step 5 ：For part (c), we need to find the critical values for a two-tailed test with α=0.10 and n=11. The degrees of freedom is n-1=10. The critical values are \(t_{\text {crit }}=\boxed{-1.812}\) and \(\boxed{1.812}\) (rounded to three decimal places).