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 20 degrees of freedom. (b) Determine the critical value(s) for a left-tailed test of a population mean at the $\alpha=0.05$ 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 $\alpha=0.01$ level of significance based on a sample size of $n=11$. Click here to view the t-Distribution Area in Right Tail. (a) $t_{\text {crit }}=\square \square$ (Round to three decimal places as needed.)

Step 1 ：The problem is asking for the critical value for a right-tailed test of a population mean at the α=0.10 level of significance with 20 degrees of freedom. The critical value is a point on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis. If the absolute value of your test statistic is greater than the critical value, you can declare statistical significance and reject the null hypothesis.

Step 2 ：For a right-tailed test, we will find the value such that the area to the right of that value (under the curve) is 0.10. Since we have 20 degrees of freedom, we will use a t-distribution with 20 degrees of freedom.

Step 3 ：We can use the t-distribution table or statistical software to find this value. The function that gives the value below which a given percentage of the data falls is used. Since we want the value above which 10% of the data falls (for a right-tailed test), we can use 1 - 0.10 = 0.90 as the input to this function.

Step 4 ：Using these parameters, the critical value is found to be approximately 1.325.

Step 5 ：Final Answer: The critical value for a right-tailed test of a population mean at the α=0.10 level of significance with 20 degrees of freedom is \(\boxed{1.325}\).