Determine Whether the Samples Are Independent or Dependent Use a 010 Significance Level to Test the Claim That the Mean

question 26

Essay

Determine whether the samples are independent or dependent.
-A researcher was interested in comparing the GPAs of students at two different colleges. Independent random
samples of 8 students from college A and 13 students from college B yielded the following GPAs: $$\begin{array} { | c | c c | } \hline \text { College A } & { \text { College B } } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 \\3.4 & \\\hline\end{array}$$ Use a 0.10 significance level to test the claim that the mean GPA of students at college A is different from the
mean GPA of students at college B. Use the P-value method of hypothesis testing. $$\text { (Note: } \left. \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , \mathrm {~s} _ { 1 } = 0.4357 , \mathrm {~s} _ { 2 } = 0.5485 . \right)$$

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Definitions:

Dissonance Paradigm

A theoretical framework used to understand the discomfort from cognitive dissonance and how individuals attempt to reduce it.

Free Choice

The ability or power to make decisions autonomously without external constraints or coercion.

Spreading Alternatives

A cognitive phenomenon where individuals devalue rejected alternatives to feel better about the choices they have made.

Self-Verification

The desire and tendency of individuals to seek confirmation of their self-concept, whether positive or negative, from their social environment.