Test the Indicated Claim About the Means of Two Populations

question 5

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. A researcher wishes to determine
whether people with high blood pressure can reduce their blood pressure, measured in mm Hg,
by following a particular diet. Use a significance level of 0.01 to test the claim that the treatment
group is from a population with a smaller mean than the control group. 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. $$\begin{array} { | l | l | } \hline \text { Treatment Group } &{ \text { Control Group } } \\\hline n _ { 1 } = 35 & n _ { 2 } = 75 \\\hline \bar { x } _ { 1 } = 189.1 & \bar { x } _ { 2 } = 203.7 \\\hline s _ { 1 } = 38.7 & s _ { 2 } = 39.2 \\\hline\end{array}$$

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Definitions:

Learned Helplessness

A condition in which an individual learns to feel powerless and stops trying to change their situation, often a result of repeated failures or lack of control.

Seligman's Model

Refers to the learned helplessness theory, proposing that individuals may learn to perceive themselves as powerless in situations of repeated failure or discomfort.

Depressed Individuals

Refers to persons who are experiencing a state of low mood and aversion to activity, significantly affecting their thoughts, behavior, feelings, and sense of well-being.

Attributes

Qualities, features, or characteristics that are inherent in or ascribed to something or someone.