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%?

Question

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%?

Quizplus · Accepted Answer

The Answer of 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%?

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