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1. In the design of an experiment we have a treatment T with four levels T1,T2, T3, T4. We are planning to use CRD model and we have only n -20 observations available How should we allocate the n observations to the four treatments to minimize the average variance of the estimated treatment eftects AV (var(i) + var(T2) + var(T3) + var(T4)) 4 Hint: Find the values of ri by minimizing Ay subject to the constraint Σに1 , nj

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In the design of an exp esiment we have a teatment with four levelsT,ך2љ, т, we are planning to use cRD Model and we have only n-0 observations available iven Thatlet us consider the CRo Madel as yij = ut Ti tEij 1 - 1, 2, 3,4 Where and EijN(0,2) The least square estimate of u and τί are iven D 1 1, 21 3,4 Since 420 2 L1 Ti 2.0 i2ing Av with tespect to Ti subject to Minimizin Condition ZT This is equivalart to minimizinahere γ 15 q Ti -20 Ti 2O 4 Dipetentiałiny ow e.t. T and esuating to ure ОТі σ2 4 Ti Adding V l s l 2, 3, y we get 1Ö utHng t

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