Find the critical value for a confidence interval with the following information: $n=19$; alpha $=0.05$. Note that answer choices are shown in the absolute value form. In other words it's the critical value without a positive/negative sign.

Step 1 ：We are given that the sample size, \(n=19\), and the significance level, \(\alpha=0.05\).

Step 2 ：The degrees of freedom is calculated as \(n-1\), which is \(19-1=18\).

Step 3 ：The alpha level is divided by 2 for a two-tailed test, so we need to find the t-value for 18 degrees of freedom and an alpha level of 0.025.

Step 4 ：The probability for the t-distribution is calculated as \(1 - \frac{\alpha}{2}\), which is \(1 - \frac{0.05}{2} = 0.975\).

Step 5 ：Using the t-distribution table or a statistical software, we find the critical value corresponding to 18 degrees of freedom and a probability of 0.975.

Step 6 ：The critical value is found to be 2.10092204024096.

Step 7 ：Final Answer: The critical value for a confidence interval with \(n=19\) and alpha \(=0.05\) is \(\boxed{2.10092204024096}\).