An experiment was conducted to compare the wearing qualities of three types of paint (A, B, and C) when subjected to the abrasive action of a slowly rotting cloth-surfaced wheel. Ten paint specimens were tested for each Paint Type and the Number of Hours until visible abrasion was apparent was recorded. Using the data below, is there evidence to indicated a difference in the three Paint Type?
Paint Type
A B C
148 513 335
76 264 643
393 433 216
520 94 536
236 535 128
134 327 723
55 214 258
166 135 380
415 280 594
153 304 465
A. State the Hypotheses.
B. Give the Test Statistic.
C. Give the P- Value
D. Make the decision.

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)=

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