There Are Different Approaches to Fitness Training A Estimate with 95% Confidence the Ratio of the Variances

question 6

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 ratio of the variances of the percentage improvement in fitness, and briefly describe what the interval estimate tells you.
b. Do these results allow us to conclude at the 5% significance level that approach 2 is superior?

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Definitions:

Expected Frequency

The number of occurrences predicted in a category of a contingency table based on probabilistic models.

Political Preference

An individual's inclination or bias toward one or more political parties, ideologies, or policy positions.

Respondents

Individuals who provide data or answers to questions in a survey or study.

One-sample Chi-square

A statistical test that determines if the observed frequencies differ significantly from the expected frequencies in one categorical dataset.