Listed below are grade averages for randomly selected students with three differ

Question

Listed below are grade averages for randomly selected students with three different categories of high-school background. Preliminary data analyses indicate that it is not reasonable to consider the assumptions for one –way ANOVA satisfied. At the 0.05 significance level, do the data provide sufficient evidence to conclude that a difference exists in the three population means? What are the required assumptions for using one –way ANOVA?

HIGH SCHOOL RECORD

Good

Fair

Poor

3.21

2.87

2.01

3.65

3.05

2.31

1.00

2.00

2.98

3.12

0.00

0.50

2.75

1.98

2.36

Good

Fair

Poor

3.21

2.87

2.01

3.65

3.05

2.31

1.00

2.00

2.98

3.12

0.00

0.50

2.75

1.98

2.36

Explanation / Answer

Assumptions for one way ANOVA :

1) Each sample must be an independent sample.

2) The distribution of response variable must follow normal distribution.

3) Variances must be equal for all groups.

The hypothesis are :

H0 : There is no difference in the three population means.

H1 : There is difference in the three population means.

Wee run one way ANOVA test in excel and we get output as follow :

Here Fcalculated = 0.8137

Fcritical = 3.8853

Here calculated value of F < critical value of F

Hence we fail to reject null hypothesis.

Conclusion : The data do not provide sufficient evidence to conclude that a difference exists in the three population means

Anova: Single Factor SUMMARY Groups Count Sum Average Variance Good 5 13.73 2.746 1.05523 Fair 5 9.9 1.98 1.46445 Poor 5 10.16 2.032 0.85777 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 1.832093 2 0.916047 0.813673 0.466251 3.885294 Within Groups 13.5098 12 1.125817 Total 15.34189 14

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