Question

A testing center at the university wants to compare the average test taking time of undergraduate students on a standardized entrance exam to graduate school. Four departments are selected, and from each department, 25 students are randomly sampled (100 students total). The center then checks for test taking time (in minutes), and compares the average test taking time of students using ANOVA. Complete the following one-factor ANOVA summary table using alpha = .05. Based on the results, do students in different departments have different departments have different test taking times?

Source	SS	df	MS	F	Critical Value and Decision
Between
Within			11
Total	1188

Answer 1

Here we are doing one way ANOVA and number of treatments here are : 4

Since departments are 4

And it is also given that there are 25 students in each department choosen for experiment.

So

Total students: 25*4 = 100

Here : Degree of freedoms will be distributed as :

Since here n = 100

so df total = n-1 = 100-1 = 99

here there are 4 treatments so

df between = 4-1 = 3

and remaining will be :

df within = 99-3 = 96

and we also know that

MS(mean square) = SS/df

for all sources of variation.

Now we can complete the table:

And the table is :

Source	SS	df	MS	F	Critical Value and Decision
Between	132	3	44	4
Within	1056	96	11
Total	1188	99

Here the test statistic F = 4 ~ F3, 96

So at

Critical value is

which we have calculated in R

Here since

which implies that we have enouh evidence to reject the null hypothesis. which implies that different departments have different test taking times is true.