Samples were drawn from three populations. The sample sizes were $n _ { 1 } = 8 , n _ { 2 } = 6$ and $n _ { 3 } = 6$ The sample means were $\bar { x } _ { 1 } = 1.92 , \bar { x } _ { 2 } = 1.34 , \text { and } \bar { x } _ { 3 } = 1.76$ The sample standard deviations were $s _ { 1 } = 0.26 , s _ { 2 } = 0.36 , \text { and } s _ { 3 } = 0.45$ The grand mean is $\overline { \bar { x } } = 1.698 .$
Compute the mean squares MSTr.
A) 0.5932
B) 4.7259
C) 2.1337
D) 1.1863

Question

Quizplus · Accepted Answer

The mean square for treatments is $$MSTr=\frac{n_1(\bar{x}_1-\overline{\bar{x}})^2+n_2(\bar{x}_2-\overline{\bar{x}})^2+n_3(\bar{x}_3-\overline{\bar{x}})^2}{k-1}$$$$=\frac{8(1.92-1.698)^2+6(1.34-1.698)^2+6(1.76-1.698)^2}{3-1}$$$$=\frac{8(0.222)^2+6(-0.358)^2+6(0.062)^2}{2}$$$$=\frac{0.392+0.798+0.234}{2}$$$$=\frac{1.424}{2}$$$$=0.712$$

Samples Were Drawn from Three Populations n1=8,n2=6n _ { 1 } = 8 , n _ { 2 } = 6n1​=8,n2​=6

Samples Were Drawn from Three Populations $n _ { 1 } = 8 , n _ { 2 } = 6$