Your ANOVA summary table should have the following setup:
Fill in the data with what you know, then find what you don't know.
Here are a few hints:
SS total = SS between + SS within
To calculate df between:
k - 1
Note: k = number of levels or groups.
To calculate df within:
N - k
Note: N = total number of values in all levels or groups.
df total = df between + df within
To calculate MS between:
SS between/df between
To calculate MS within:
SS within/df within
To calculate F-ratio:
MS between/MS within
After filling in the table and finding the F-ratio, find the critical or cutoff value to reject the null using an F-table. Compare to the F-ratio to determine whether or not to reject the null. If the null is rejected, there is a difference. If the null is not rejected, there is no difference.
If you need to use the Tukey procedure, compare all possible pairs of means to determine which majors differ.
I hope this brief summary will get you started.
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