To discourage cheating a professor makes three different ver

To discourage cheating, a professor makes three different versions of an exam. For the 105 students in her class. She makes 35 copies of each student. After the exam, the professor is scrambled, and copy is given to each student. After the exam, the professor is concerned that one version might have been easier than the others. She uses a one-way ANOVA to the test whether the average score was different for the three versions. The ANOVA table and a boxplot of the results are below. What hypotheses are tested by this ANOVA? Write a the sentence describing the of the conclusion of the test in the context of this problem.

Solution

let the three versions of the exams be denoted by A,B,C

let the average score for the version A be u1

the average score for the version B be u2

the average score for the version C be u3

the professor wants to test whether the average score was different for the different versions.

a) so the hypothesis for testing the professor\'s interest

null hypothesis H0: u1=u2=u3          vs alternative hypothesis H1: not H0

b) to test the hypothesis a one-way anova table is constructed.

there are 105 students in total

from the table we find SSA: sum of squares due to different versions of exams=771.943 with df=2

SSE: sum of squares due to error=8883.49 with df=102

therefore MSA=mean square due to different versions of exams=SSA/2=385.971

MSE=mean square due to error=SSE/102=87.093

so the F ratio is F=MSA/MSE=4.4317 which under H0 follows an F distribution with df 2 and 102

so the p value is P[F>4.4317]=0.0143  

taking level of significance =alpha=0.05 we get

p value<alpha

hence the null hypothesis is rejected

hence the conclusion is :

based on the given data at hand at 5% level of significance the null hypothesis is rejected and it is concluded that the average scores were different for the three different versions of exam