Test the Claim That the Samples Come from Populations with the Same

question 54

Essay

Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance.
-Given the sample data below, test the claim that the populations have the same mean. Use a significance level of 0.05. $$\begin{array} { l } \text { Brand A }& \text { Brand B } &\text { Brand C } & \text { Brand D } \\{ n = 16 } &{ n = 16 } & { n = 16 } &{ n = 16 } \\\bar { x } = 2.09& \bar { x } = 3.48 & \bar { x } = 1.86 & \bar { x } = 2.84 \\s = 0.37 & \mathrm {~s} = 0.61& \mathrm {~s} = 0.45 & \mathrm {~s} = 0.53 \\\end{array}$$

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Definitions:

Mental Exercises

Activities designed to improve cognitive functions such as memory, focus, and problem-solving skills.

Trancelike State

A state of deep relaxation or hypnosis in which an individual may be more open to suggestions and less aware of their surroundings.

Activation-information-mode Model

A theory suggesting that dreams are initiated in the brain's pons and that their content is affected by the dreamer's personal life and experiences.

Dreams

Successions of images, ideas, emotions, and sensations occurring involuntarily in the mind during certain stages of sleep.