Suppose that a study compares the means of two groups. There are 40 males in Group 1 and 35 females in Group 2. The degrees of freedom for this study when using the t-test for the difference between means is:

Question

BlackTom AI · Accepted Answer

When comparing the means of two independent groups with a t-test, the common approach is to use the pooled-variance t-test which assumes equal variances; the degrees of freedom in that case are n1 + n2 − 2. Here, Group 1 has 40 individuals and Group 2 has 35 individuals, so the calculation is 40 + 35 − 2 = 73.

Option a. 73: This matches the standard formula for the simple two-sample t-test with equal variances and uses all observations from both groups minus 2 for the estimated means. It is therefore the correct df in this scenario.

Option b. 74: A tempting miscalculation could come from adding the group sizes and then subtracting 1, i.e., 40 + 35 − 1 = 74. However, that would correspond to degrees of freedom for estimating a single pooled mean, which is not the usual df formula for the two-sample t-test.

Option c. 75: This would result from subtracting 2 from a total of 77 observations, which would imply a total sample size of 77. But the actual total is 40 + 35 = 75 observations, so df cannot be 75 in this standard setup.

Option d. 72: This option reflects subtracting 3 from the total sample size 75, which does not align with the standard df calculation for a two-sample t-test with equal variances. It would suggest two fewer parameters estimated beyond the two group means, which is not the usual practice here.

In summary, the correct degrees of freedom for a two-group means comparison with n1 = 40 and n2 = 35 is 73, since you pool the two sample sizes and subtract 2 for the two estimated means.

Suppose that a study compares the means of two groups. There are 40 males in Group 1 and 35 females in Group 2. The degrees of freedom for this study when using the t-test for the difference between means is:单项选择题

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