There Are Different Approaches to Fitness Training A Estimate with 95% Confidence the Mean Percentage Improvement with One

question 83

Essay

There are different approaches to fitness training. To judge which one of two approaches is better, 200 25-year-old men were randomly selected to participate in an experiment. For four weeks, 100 men were trained according to approach 1 while the other 100 men were trained according to approach 2. The percentage improvement in fitness was measured for each man and the statistics shown below were computed. The percentage figures are known to be normally distributed. $$\begin{array} { | c | c | } \hline \text { Approach 1 } & \text { Approach } 2 \\\hline \bar { x } _ { 1 } = 27.3 & \bar { x } _ { 2 } = 33.6 \\\hline s _ { 1 } ^ { 2 } = 47.614 & s _ { 2 } ^ { 2 } = 28.09 \\\hline\end{array}$$ a. Estimate with 95% confidence the mean percentage improvement with approach 2.
b. Do these results allow us to conclude at the 5% significance level that the mean percentage improvement with approach 1 is at least 25%?

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Definitions:

Reference Groups

Groups that individuals compare themselves to or use as a standard for evaluating their own values, attitudes, and behaviors.

Interpersonal Group Therapy

A form of therapy focusing on the interactions and relationships among group members, to address and improve mental health issues.

Psychodrama

A form of therapy where people act out their experiences and emotions as part of a group to achieve catharsis or insight.

Storming Stage

The second phase in the Tuckman's stages of group development, characterized by conflict and competition as group members come to terms with their roles.