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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.

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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.

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Using a t-distribution calculator, it is found that the critical value is of t = 1.684.

  • When there are multiple groups, the total amount of degrees of freedom is the sum of the number of degrees of freedom of each group.

In this problem, the first group has 19 df, while the second group has 21 df. Hence, in total, there are 19 + 21 = 40 df.

  • The level of significance is [tex]\alpha = 0.05[/tex].
  • We want to cut-off the upper 2.5%, hence, it is a right-tailed test.

Using a t-distribution calculator, with a right-tailed test, 40 df and [tex]\alpha = 0.05[/tex], the critical value is t = 1.684.

A similar problem is given at https://brainly.com/question/16103798

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