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:

Specific Evidence

Evidence that relates to a particular issue or fact, used to support or refute a claim in legal or formal proceedings.

Administrative Investigation

An inquiry conducted by an organization or agency to uncover facts or information about a particular matter, often related to misconduct.

Relevant Information

Data or facts that are directly related to and significant for the matter at hand.

Federal Agency

A government body established by Congress to perform a specific function or set of functions at a national level.