Ms. Smith teaches three Algebra 1 classes that cover exactly the same content. She is wondering if changing the order of some of the lessons would be beneficial to students. In class A, she teaches everything in the traditional order. In class B, she decides to skip Chapter 1 as it is preliminary information that students may already know. In class C, she decides to do Chapter 5 prior to doing Chapter 3. She would like to know if there are any significant differences in the average scores of the three classes.

Since we need to compare more than two population means so one way ANOVA will be used.
Following is the output of one way ANOVA:
Anova: Single Factor  
SUMMARY  
Groups  Count  Sum  Average  Variance  
Class A  25  1333.89  53.3556  788.9803173  
Class B  25  1239.43  49.5772  705.9474877  
Class C  25  1036.75  41.47  571.4606583  
ANOVA  
Source of Variation  SS  df  MS  F  Pvalue  F crit 
Between Groups  1843.920715  2  921.9603573  1.338509734  0.268682  3.123907 
Within Groups  49593.32312  72  688.7961544  
Total  51437.24383  74 
The pvalue of F test is:
pvalue = 0.2687
Since pvalue is greater than 0.05 so we cannot conclude that there is a significant differences in the average scores of the three classes.
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