Construct a confidence interval for d, the mean of the differences d for the population of paired data. Assume that the population of paired differences is normally distributed.

A coach use a new technique in training middle distance runners. The times for 9 different athletes to run 800 meters before an after this training are shown below :

Athlete | A B C D E F G H I

Time before training(seconds) | 115.2 120.9 108.0 112.4 107.5 119.1 121.3 110.8 122.3

Time after training (seconds) | 116.0 119.1 105.1 111.9 109.1 115.2 118.5 110.7 120.9

a) Find the difference data, di= before - after

Athlete | A B C D E F G H I

di |

b) construct a 90% confidence interval for d