Test the Indicated Claim About the Means of Two Populations

question 44

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. $\begin{array} { l | c c } \text { College A } & { \text { College B } } \\\hline 3.7 & 3.8 & 2.8 \\3.2 & 3.2 & 4.0 \\3.0 & 3.0 & 3.6 \\2.5 & 3.9 & 2.6 \\2.7 & 3.8 & 4.0 \\3.6 & 2.5 & 3.6 \\2.8 & 3.9 & \\3.4 & &\end{array}$ 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. $\left( \text { Note: } \bar { x } _ { 1 } = 3.1125 , \bar { x } _ { 2 } = 3.4385 , s _ { 1 } = 0.4357 , s _ { 2 } = 0.5485 . \right)$ 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:

Cellular Immunity

Is a component of the immune system that involves the activation of immune cells to combat pathogens, distinct from antibody-mediated immunity.

Interpersonal Success

Achieving positive outcomes in interactions with others, often characterized by effective communication and mutual respect.

Insurmountable Stressors

Insurmountable Stressors are extreme stress factors that individuals perceive as beyond their capability to manage or overcome, often leading to significant distress or dysfunction.

Sporadic Stressors

Random or irregularly occurring stresses that can impact an individual's psychological or physical well-being.