Answer to Question #30149 in Statistics and Probability for siti khadijah

Question

A dietitian wanted to test three different diets to find our whether or not the mean weight loss for each of these diets is the same. He randomly selected 15 overweight individuals, randomly divided them into three groups, and put each group on one of the three diets. The table shown below records the weights loss by these individuals after being on these diets for six weeks.
Diet A Diet B Diet C
7 4 15
10 3 12
4 6 17
6 4 16
8 7 11

By using ANOVA procedure, we wish to test the null hypothesis that the mean weight loss by all individuals on each of the three diets is equal. The significance level is 2.5%.

Answer 1

We find the numerical characteristics of randomdata independent samples:
x = 7+10+4+6+8/5 = 7
y = 4+3+6+4+7/5 = 4.8
z = 15+12+17+16+11/5 = 14.2
Dx = (7-7)^2+(10-7)^2+(4-7)^2+(6-7)^2+(8-7)^2/5 = 4
Dy = (4-4.8)^2+(3-4.8)^2+(6-4.8)^2+(4-4.8)^2+(7-4.8)^2/5 = 2.16
Dz = (15-14.2)^2+(12-14.2)^2+(17-14.2)^2+(16-14.2)^2+(11-14.2)^2/5=5.36
We find the observed value of the test:
Z = z - x - y / sqr(Dx/n +Dy/m + Dz/k) = 2.4/sqr(0.8 +0.432 + 1.072) = 1.52
We find the critical point:
f(Z) = 1 - a / 2 = 1 - 0.025/2 = 0,4875
from the Laplace function table we find
Zcr =1.99
1.52<1.99
the null hypothesis of equal performance of the three groups is confirmed.