17. School system A school district superintendent wants to test a new method of teaching arithmetic in the fourth grade at his 15 schools. He plans to select 8 students from each school to take part in the experiment, but to make sure they are roughly of the same ability, he first gives a test to all 120 students. Here are the scores of the test by school:

The ANOVA table shows:
Source DF Sum of Squares Mean Square F-Ratio P-Value School 14 108.800 7.7714 1.0735 0.3899 Error 105 760.125 7.2392 Total 119 868.925

a) What are the null and alternative hypotheses?

b) What does the ANOVA table say about the null hypothesis? (Be sure to report this in terms of scores and schools.)

c) An intern reports that he has done t-tests of every school against every other school and finds that several of the schools seem to differ in mean score. Does this match your finding in part b? Give an explanation for the difference, if any, of the two results.

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