Answer:
A) H0: mean of A= mean of B= mean of C
H1: all means are unequal
B) 3.48194
C) 0.04515
D) H0 is accepted. There is significant difference among mean hours after which visibile abrasion is observed for each type of paint
Step-by-step explanation:
A) Here Anova test will be used as we are comparing three groups
B) mean of A= 229.6, SD of A= 158.1962, SE of A= 50.026
mean of B= 309.9 , SD of B= 147.8742, SE of B= 46.7619
mean of C= 427.8, SD of C= 196.8179, SE of C= 62.2393
overall mean= 322.43
degrees of freedom between groups= 3-1=2
degrees of freeddom of error= total number of observations - number of groups= 30-3= 27
total degrees of freedom= total number of samples-1= 30-1 =29
Sum of squares between groups=∑ sample size of group×(individual group mean- over all mean)²
=198772.4667
mean of sum of squares between groups= sum of squares between groups/ (number of groups -1)
= 198772.4667/2
sum of squares of error=∑∑ (individual observation of group- group mean)²
= 770670.9223
mean sum of squares of erros= sum of squares of error/(total number of samples-number of groups)
= 770670.92/27
= 28543.38
F- stat= mean sum of squares between groups/ mean sum of squares of error
F stat= 3.48194
C) p- value= 0.04515
D) since F-stat is greater than p- value, null hypothesis is rejected
from F distribution table
F(2,27)=
