Find the critical value(s) for the type of t-test with level of significance $\alpha$ and sample size $n$. \[ H_{a}: \mu \neq 20, \alpha=0.01, n=12 \] A. \pm 2.718 B. \pm 1.796 C. \pm 3.106 D. \pm 2.201

Step 1 ：The critical value for a t-test can be found using the t-distribution table. The degrees of freedom for this test is n-1, which is 12-1=11. The level of significance is 0.01, and since this is a two-tailed test (because the alternative hypothesis is \(\mu \neq 20\)), we need to divide the level of significance by 2 to find the critical value from the t-distribution table. So, we need to find the t-value corresponding to a cumulative probability of 1 - 0.01/2 = 0.995 with 11 degrees of freedom.

Step 2 ：df = 11

Step 3 ：p = 0.995

Step 4 ：critical_value = 3.1058065132211006

Step 5 ：The critical value for the t-test with 11 degrees of freedom and a level of significance of 0.01 (two-tailed) is approximately 3.106. This matches with option C in the question.

Step 6 ：Final Answer: The critical value(s) for the type of t-test with level of significance \(\alpha\) and sample size \(n\) is \(\boxed{\pm 3.106}\).