Answer to Question #284620 in Statistics and Probability for mekna

Question

Groups of men from three different areas of the country are to be tested for mean weight. The entries in the Table 1 are the weights for the different groups.

Group 1 : 216 , 198 , 240 , 187 , 176

Group 2 : 202 , 213 , 284 , 228 , 210

Group 3 : 170 , 165 , 182 , 197 , 201

a)What is the Sum of Squares Factor?

b)What is the Sum of Squares Error?

c)What is the df for the numerator?

d)What is the df for the denominator?

e)What is the Mean Square Factor?

f)What is the Mean Square Error?

g)What is the F statistic?

Answer 1

a)

$SSG=\sum n_i(\overline{x}_i-\overline{x})^2=4939.2$

where

$n_i$ is size of group,

$\overline{x}_i$ is average of group,

$\overline{x}$ is overall average

b)

$SSE=\sum (n_i-1)s_i^2=7920.4$

where

s_i is standard deviation of group

c)

$df_1=k-1=3-1=2$

where

k is number of groups

d)

$df_2=n-k=15-3=12$

where

n is overall sample size

e)

$MSG=SSG/(k-1)=2469.6$

f)

$MSE=SSE/(n-k)=660.0$

g)

$F=MSG/MSE=3.7416$