Question

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 1	School 2	School 3	School 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.

Answer 1

a) NULL HYPOTHESIS H0:

ALTERNATIVE HYPOTHESIS Ha: Not all means are equal

b) test statistic= 7.739

P value= 0.002

c) Since P value is SMALLER THAN THE LEVEL OF SIGNIFICANCE therefore SIGNIFICANT.

Decision: REJECT NULL HYPOTHESIS H0.

Conclusion: We have sufficient evidence to conclude that there is difference in mean scores.

d) From Bonferroni 's test there is difference in SCHOOL 1 and School 3 , School 2 and School 3, and School 3 and School 4.