Question

In: Math

Mr Ahuja have always been interested in whether or not where a student sits is related...

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.

Solutions

Expert Solution

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.


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