A Coach Uses a New Technique in Training Middle Distance

question 35

Essay

A coach uses a new technique in training middle distance runners.The times for 8 different athletes to run 800 metres before and after this training are shown below. $$\begin{array} { c | c c c c c c c c } \text { Athlete } & \mathrm { A } & \mathrm { B } & \mathrm { C } & \mathrm { D } & \mathrm { E } & \mathrm { F } & \mathrm { G } & \mathrm { H } \\\hline \begin{array} { c } \text { Time before training } \\\text { (seconds) }\end{array} & 115.6 & 115.6 & 113.7 & 118.6 & 118 & 119.9 & 110.7 & 119.5 \\\hline \begin{array} { c } \text { Time after training } \\\text { (seconds) }\end{array} & 116.2 & 114.3 & 111.3 & 119.4 & 116.2 & 120 & 107.1 & 115.6\end{array}$$ Do the data suggest that,on average,the training helps to improve the athletes' times for the 800 metres? Perform a paired $\text { t-test }$ at the 5% significance level.

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Definitions:

Mean

The average of a set of numbers, calculated by dividing the sum of all the numbers by the count of the numbers.

Price Per Gallon

The cost of one gallon of a substance, often used in the context of fuel pricing.

Skewness

Skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean, indicating whether the data distribution leans to the left or the right.