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

question 74

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:

Productive Capacity

The maximum output or production level that can be achieved with the available inputs and resources without stressing the production system.

Direct Method

A method for presenting cash flows related to operating activities, highlighting the main categories of gross cash inflows and outflows.

Operating Activities

Activities that are directly related to the operation of the business, such as sales, services, and administrative tasks, distinguishing them from investing and financing activities.

Economic Benefits

Inflows of assets or reductions in liabilities that result in an increase in equity, other than those relating to contributions from equity participants.