Samples were drawn from three populations. The sample sizes were n₁=8, n₂=8, and n₃=7 . The sample means were $\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95$ , and $\bar { x } _ { 3 }$=2.57 . The sample standard deviations were s₁=0.27, s₂=0.45, and s₃=0.25 . The grand mean is =2.055217. i). Compute the sums of squares SSTr and SSE. ii). How many degrees of freedom are there for SSTr and SSE? iii). Compute the sums of squares MSTr and MSE. iv). Compute the value of the test statistic F. v). Can you conclude that two or more of the population means are different? Use the $\alpha = 0.05$ level of significance.

Question

Quizplus · Accepted Answer

The Answer is i). SSTr = 2.8970; SSE = 2.3028
ii). degrees of freedom for SSTr = 2; degrees of freedom for SSE = 20
iii). MSTr = 1.4485; MSE = 0.1151
iv). 12.580
v). Yes

Samples Were Drawn from Three Populations xˉ1=1.71,xˉ2=1.95\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95xˉ1​=1.71,xˉ2​=1.95

Samples Were Drawn from Three Populations $\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95$