To obtain the critical values for a specific statistical test, we first need to know the type of the test used and the significance level. However, assuming the use of a two-tailed t-test with a significance level of 0.05, we can proceed as follows:
1. Identify the degrees of freedom for the t-test. For instance, if there are 10 observations, the degrees of freedom would be 9 as it is equal to the number of observations minus 1.
2. Identify the significance level. In our case, it's given to be 0.05.
3. Given this is a two-tailed test, divide the significance level by 2. Therefore, the alpha value becomes 0.05/2 = 0.025.
4. To find the critical values, it's necessary to know they are the values such that the area under the t-distribution to the left of the lower critical value and to the right of the upper critical value equals alpha (0.025).
5. Compute these values using the inverse of the cumulative distribution function. You can use statistical tables or statistical software for doing this.
6. The lower critical value is calculated by finding the t-value that has an area to its left equal to alpha (0.025) on the t-distribution with the identified degrees of freedom.
7. The upper critical value is calculated by finding the t-value that leaves an area to its right equal to alpha (0.025) on the t-distribution with the identified degrees of freedom.
Remember, your critical values might be negative or positive depending on the t-distribution table or software you are using. These values then are utilized for hypothesis testing to decide whether to reject or fail to reject the null hypothesis.