**Instructions**: Compute critical t values for the t-distribution using the form below. Please type significance level \(\alpha\), number of degrees of freedom and indicate the type of tail (left-tailed, right-tailed, or two-tailed)

More information about *critical values for the t-distribution*: Critical values are points at the tail(s) of a specific distribution, with the property that the area under the curve for those critical points in the tails is equal to the given value of \(\alpha\) The distribution in this case is the T-Student distribution. In general terms, for a two-tailed case, the critical values correspond to two points to the left and right of the center of the distribution, that have the property that the sum of the area under the curve for the left tail (from the left critical point) and the area under the curve for the right tail is equal to the given significance level \(\alpha\).

For a left-tailed case, the critical value corresponds to the point to the left of the center of the distribution, with the property that the area under the curve for the left tail (from the critical point to the left) is equal to the given significance level \(\alpha\).

For a right-tailed case, the critical value corresponds to the point to the right of the center of the distribution, with the property that the area under the curve for the right tail (from the critical point to the right) is equal to the given significance level \(\alpha\).

The main properties of the T-distribution and its critical points are:

- The t-distribution is a symmetric, continuous distribution, that is determined by the number of degrees of freedom (df)
- The t-distribution converges (in a distributional sense) to the standard normal distribution (Z-distribution) as the degrees of freedom (df) converge to infinity
- The t-distribution is used for various t-tests, where the population standard deviation is not known
- Since the t-distribution is symmetric, the critical points for the two-tailed case are symmetric with respect to the center of the distribution
- Also, since the t-distribution is symmetric, finding critical values for a two-tailed test with a significance of \(\alpha\) is the same as finding one-tailed critical values for a significance of \(\alpha\)/2