A school district superintendent wants to test a new method of teaching arithmet

Question

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 the same ability, he gives a test to all 120 students. Here are the test by school and the ANOVA table.

The ANOVA table shows:

Analysis of Variance

A). What are the null hypothesis and alternative hypothesis?

B). What does the ANOVA table say about the null hypothesis?

C). An intern reports that he has done t-tests of every school against every other school and finds that several of the schools seems to differ in mean score. Does this match your findings in part B?

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

Explanation / Answer

A). What are the null hypothesis and alternative hypothesis?

Null hypothesis: all means are eqaul

Alternative hypothesis: at least one mean is different

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B). What does the ANOVA table say about the null hypothesis?

Assume that the significant level a=0.05

Since the p-value of F test is 0.3899 which is greater than 0.05, we do not reject the null hypothesis.

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C). An intern reports that he has done t-tests of every school against every other school and finds that several of the schools seems to differ in mean score. Does this match your findings in part B?

Yes, this match my findings in part B

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