Answer to Question #18616 in Quantitative Methods for Elu

Question

After running about 17 miles, marathon runners encounter a form of physiological stress which they call “hitting the wall.” To better pinpoint where in a race to expect this phenomenon, a sports physiologist has 12 male marathon runners race until each feels this stress. The variable of interest is the number of miles run until the stress occurs. These are 15.8 16.5 15.3 16.2 17.1 16.4 17.5 17.3 16.9 16.6 17.0 17.7 Construct the 95% confidence interval from the data.
Expert's answer

Answer 1

Mean value for this data is 16.6917
After that we calculate sigma (square root of dispersion)
Sqrt(Mean(data^2)-Mean(data)^2)=0.673867
As known, 95% interval is for 2 sigma.
So, 2*0.673867 is 1.34, that is 95% confidence interval (in case of normal distribution)