In: Math
Mr Ahuja have always been interested in whether or not where a student sits is related to the students overall grades in school. Below is a table that divides students into 3 seating areas: Front, Middle, and Back with their given GPAS.
Front Middle Back
3.062 2.859 2.583
3.894 2.639 2.653
2.966 3.634 3.09
3.575 3.564 3.06
4 2.115 2.463
2.69 3.08 2.598
3.523 2.937 2.879
3.332 3.091 2.926
3.885 2.655 3.221
3.559 2.526 2.646
Calculate a One-Way ANOVA table (using EXCEL) for the data above. Complete the following: At α = .05, test to see if there is a significant difference among the average GPA of all the students based on three areas of seating. Use both the critical and p-value approaches. Include hypotheses, critical values, results, and conclusions in the language of the problem.
To test
against H1 : at least one mean is different
Using Excel, (Data -> Data Analysis -> Anova: Single Factor), we get the following output -
Now,
The value of test statistic F = 7.50238
and P-value = 0.0026
and critical value = 3.354
Since P-value < 0.05 and F statistic > critical value, we reject the null hypothesis at 5% level of significance and we can conclude that there is a significant difference among the average GPA of all the students based on three areas of seating.