Fitness Training There are different approaches to fitness training. To judge which one of two appro

Question: Fitness Training

There are different approaches to fitness training. To judge which one of two approaches is better, 200 twenty-five year old men are randomly selected to participate in an experiment. For four weeks, 100 men are trained by approach 1 while the other 100 men are trained by 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.

Approach 1	Approach 2
\[{{\bar{x}}_{1}}=\]27.3	\[{{\bar{x}}_{2}}=\]33.6
\[s_{1}^{2}=\]47.614	\[s_{2}^{2}=\]28.09

a) Do these results allow us to conclude at the 10% significance level that approach 2 is superior?

b) Estimate with 95% confidence the mean percentage improvement with approach 2. Interpret the interval. (Percentage improvement is what we measured -- it is our variable; don’t let the wording here make it seem more complicated than it is.)

c) Scientists are interested in determining which of the two approaches more consistently improves fitness. Do these results allow us to conclude at the 5% significance level that approach 2 results in a more consistent improvement in fitness than approach 1?

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