An experiment was conducted to examine the effect of a set of 3 treatments on subjects. 47 subjects were part of the study and randomly assigned one of the 3 treatments (treatments are labelled A, B and C). Define the data and parameters with, where 1, 2, 3; and j = 1, 2,..., Nj. Yij ;= observed response from the jth subject using the ith treatment. i = mean response of subjects using treatment i. The treatments are to be analysed using an ANOVA model. Suppose a colleague is unsure which statistical model to use for the data to use and writes down five models labelled (a) - (e) below, Model (a) Yijo+i. +ij where Yiii.i.d Sii tni-1 Model (b) Y = Y.+ij where ij i.i.d. N(0,0) Model (c): Yij = Y.+ij Model (d): Yij = Bo+i. +ij Model (e): Yijfli +ij i. Select the appropriate statistical model to describe the data and apply an ANOVA (F-test). ii. Select the appropriate null hypotheses for an ANOVA (F-test). iii. Select the appropriate alternative hypotheses for an ANOVA (F-test). OHO 12 M3 OH = = 3 = 0 Ho 143 #0 OHo =2 = 3 OH :not all are equal OH 2 143 OH = = fl3 = 0 OH = = fl3 OH 3 #0 OHnot all i are equal iv. Fill out the missing parts of the partial ANOVA table below. Write each of your answers to at least 3 decimal places: Sum Sq 16.2664 Source d.f. Treatment Residual 44 554.5907 Mean Sq 8.1332 F-stat 0.6453 Total 46 Yiii.i.d where tni-1 Sni i.i.d. where ij N(0,0) i.i.d. where ij N(0,0) Suppose a different experiment was conducted to examine the effect of a set of 3 treatments on subjects. 52 subjects were part of the study and randomly assigned one of the 3 treatments (treatments are labelled A, B and C). The sample mean y., sample standard deviation s; and the sample size n of each treatment group is given as follows. 341 Treatment A 17.6 Si n 4.17 15 Treatment B 11.8 1.74 19 Treatment C 27 18.44 18 The overall mean is given as follows: y.. = 18.73.