Data Collectionhard
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A survey with 30% missing data uses multiple imputation (M = 5). The point estimates of mean household income across 5 completed datasets are: Qˉ1=52,000,Qˉ2=51,500,Qˉ3=52,500,Qˉ4=51,800,Qˉ5=52,200\bar{Q}_1 = 52,000, \bar{Q}_2 = 51,500, \bar{Q}_3 = 52,500, \bar{Q}_4 = 51,800, \bar{Q}_5 = 52,200. The within-imputation variance (averaged over imputations) is Uˉ=1,200,000\bar{U} = 1,200,000 and between-imputation variance is B=40,000B = 40,000. By Rubin's formula, total variance is: T=Uˉ+(1+1M)BT = \bar{U} + \left(1 + \frac{1}{M}\right)B

What is the total variance estimate?