Test the Indicated Claim About the Means of Two Populations

question 157

Essay

Test the indicated claim about the means of two populations. Assume that the two samples are independent
simple random samples selected from normally distributed populations. Do not assume that the population
standard deviations are equal. $$\begin{array} { | l | c c | } \hline \text { College A } & { \text { College B } } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & & \\\hline\end{array}$$ 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. (Note: $\bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485$ .) Include your null and alternative hypotheses, the test statistic, $p$ -value or critical value(s), conclusion about the null hypothesis, and conclusion about the claim in your answer.

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Definitions:

Gordon Growth Model

The Gordon Growth Model is a method to determine the intrinsic value of a stock based on a future series of dividends that grow at a constant rate.

Fisher Effect

An economic theory that describes the relationship between inflation and both real and nominal interest rates.

Real Rate of Return

The annual percentage profit earned on an investment, adjusted for changes in prices due to inflation or other external effects.

Effective Annual Rate

The interest rate on a loan or investment, adjusted for the effect of compounding over a given period.