When Y1i , for i = 1, 2,..., n, and Y2i , for i = 1, 2,..., n, represent independent
Chapter 12, Problem 12.11(choose chapter or problem)
When Y1i , for i = 1, 2,..., n, and Y2i , for i = 1, 2,..., n, represent independent samples from two populations with means 1 and 2 and variances 2 1 and 2 2 , respectively, we determined that 2 (Y 1Y 2) = (1/n)(2 1 + 2 2 ). If the samples were paired and we computed the differences, Di , for i = 1, 2,..., n, we determined that (2/D) = (1/n)(2 1 + 2 2 212). a When is 2 (Y 1Y 2) greater than (2/D)? b When is 2 (Y 1Y 2) equal to (2/D)? c When is 2 (Y 1Y 2) less than (2/D)? d Based on the discussion in the text and your answers to parts (a)(c), when would it be better to implement the matched-pairs experiment and when would it be better to implement the independent samples experiment?
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