Three Universities Administer the Same Comprehensive Examination to the Recipients $\alpha$

question 56

Essay

Three universities administer the same comprehensive examination to the recipients of MS degrees in psychology. From each institution, a random sample of MS recipients was selected, and these recipients were then given the exam. The following table shows the scores of the students from each university. Note that the sample sizes are not equal.
a.Compute the overall mean .
b.At $\alpha$ = 0.01, test to see if there is any significant difference in the average scores of the students from the three universities. Use both the critical value and p-value approaches.

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Definitions:

Existential Instantiation

A logical process in formal argumentation where an existential quantifier (e.g., "there exists") leads to the establishment of an instance of its subject.

Universal Instantiation

A logical rule that allows for the conclusion that a general statement applies to a specific instance.

Existential Generalization

A logical operation that infers the existence of at least one member of a domain that satisfies a given property from a particular case or instance.

Quantifier Negation

A transformation in formal logic that involves altering the scope of negation in relation to quantifiers in a statement.