Say you're going to conduct a procedure for the difference between the means of two populations. You decide the samples, of sizes 12 and 15, are independent. Which of the following statements are true?
1. If we pool variances, the number of degrees of freedom is 25. II. If we don't pool variances, and we don't have access to software to compute degrees of freedom, the number of degrees of freedom is 11. III. For a given level of confidence C, a confidence interval based on 11 degrees of freedom will be wider than one based on 25 degrees of freedom.
A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
E. I, II, and III
1. If we pool variances, the number of degrees of freedom is 25, which is true.
2. If we don't pool variances and have 12 and 15 samples, the number of degrees of freedom is calculated as (N1 - 1) + (N2 - 1) = 11, so this statement is also true.
3. For a given level of confidence, a confidence interval based on fewer degrees of freedom (in this case, 11) will be wider than one based on more degrees of freedom (25), so this statement is true as well.