Foramatched pairs t test (Exercise5 16),let 2 var(Yi1) var(Yi2) and corr(Yi1, Yi2) Using theresultfromExercise2 63thatfortworandomvariables Y1 and Y2, var(Y1 Y2) var(Y1) var(Y2) 2cov(Y1, Y2), showthatvar(Y 1 Y 2) var (d) 22(1 ) n Explainhow this indicates that precisionforestimating 1 2 can bemuchbetterforhighlypositively correlated dependentsamplesthanforindependentsamples

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Question: Foramatched-pairs t test (Exercise5.16),let 2 = var(Yi1) = var(Yi2) and = corr(Yi1, Yi2). Using theresultfromExercise2.63thatfortworandomvariables Y1 and Y2, var(Y1 Y2) = var(Y1) +

Foramatched-pairs t test (Exercise5.16),let σ2 = var(Yi1) = var(Yi2) and ρ = corr(Yi1, Yi2).

Using theresultfromExercise2.63thatfortworandomvariables Y1 and Y2, var(Y1 − Y2) =

var(Y1) + var(Y2) − 2cov(Y1, Y2), showthatvar(Y 1 − Y 2) = var

(d) = 2σ2(1 − ρ)~n. Explainhow this indicates that precisionforestimating μ1 − μ2 can bemuchbetterforhighlypositively correlated dependentsamplesthanforindependentsamples.

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