Use the Traditional Method of Hypothesis Testing to Test the Given

question 19

Essay

Use the traditional method of hypothesis testing to test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations.
-Five students took a math test before and after tutoring. Their scores were as follows. $$\begin{array} { c | c c c c c } \text { Subject } & \text { A } & \text { B } & \text { C } & \text { D } & \text { E } \\\hline \text { Before } & 76 & 68 & 68 & 70 & 71 \\\hline \text { After } & 80 & 77 & 66 & 73 & 83\end{array}$$ Using a 0.01 level of significance, test the claim that the tutoring has an effect on the math scores.

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Definitions:

Basic Psychological Needs

Fundamental needs that include competence, autonomy, and relatedness, which are essential for psychological health and well-being.

Autonomy

The capacity to make an informed, uncoerced decision independently, often related to personal or organizational freedom.

Autonomy Support

A management or teaching style that nurtures self-initiation and emphasizes the importance of personal choice, freedom, and volition in carrying out tasks.

Personal Initiative

An individual's action that is anticipatory, self-starting, and persistent in overcoming barriers and implementing change or innovation.