Test the Indicated Claim About the Means of Two Populations

question 39

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. $\begin{array} { c | c c } \text { College A } & { \text { College B } } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & &\end{array}$


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:

Actual Earnings

The real income a company generates from its business activities, distinct from its reported or projected earnings.

Earnings Capitalization

A method for valuing a company by dividing its annual earnings by a certain capitalization rate, reflecting the investment's expected rate of return.

Value-Irrelevant

pertains to information or aspects that do not affect an entity's market value or decision-making process.

Restructured Earnings

Earnings that have been adjusted to reflect the impact of significant changes or reorganizations within a company, often excluding non-recurring items to better represent ongoing profitability.