Imagine that a researcher appropriately conducts a two-tailed, independent-samples t test with an alpha level of 0.05 (5%). The first group has degrees of freedom equal to 19. The second group has degrees of freedom equal to 21. What is the critical value (as a t statistic) that would cut off the upper 2.5% of the corresponding sampling distribution. Please provide three decimal places when reporting your answer.

For the first group, with 19 degrees of freedom, the critical value is t=2.093.

For the second group, with 21 degrees of freedom, the critical value is t=2.080.

Step-by-step explanation:

The critical value of the t-statistic depends on the significance level and the degrees of freedom of the sample.

For a significance level of 0.05, for a two-tailed test, there is an upper 2.5% and a lower 2.5%.

For the first group, with 19 degrees of freedom, the critical value is t=2.093.

For the second group, with 21 degrees of freedom, the critical value is t=2.080.