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An experiment was designed to compare the effectiveness of teaching statistics

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An experiment was designed to compare the effectiveness of teaching statistics in 4 different schools. Randomly selected 80 students (20 students from each school) were required to complete 5 tasks. For each given task, the average result for each of 4 schools are presented in the table below.

School 1School 2School 3School 4

81  84  56  83

76  75  60  77

77  83  65  79

85  88  68  86

93  90  80  91

a) State the null and alternative hypotheses required to test if the effectiveness of teaching are significantly different between any of the schools.
b) Carry out the ANOVA, and report the test statistic and P-value.
c) Write a brief conclusion of the ANOVA analysis.
d) Carry out the Bonferroni’s multiple comparisons and summarise the results, if appropriate.

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