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Q59Section B (Part B)59 of 120

Sampling theory — comparing sampling with and without replacement

Consider a finite population of size N=100N=100. Let T1T_1 be the sample mean of a study variable based on a sample of size nn (1<n<N)(1<n<N) under simple random sampling with replacement scheme. Let T2T_2 be the sample mean of the same study variable based on a sample of size nn under simple random sampling without replacement scheme. If Var⁡(T1)=9Var⁡(T2)\operatorname{Var}(T_1)=9\operatorname{Var}(T_2), then the sample size nn equals

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