A coach uses a new technique in training middle distance runners.The times for 9 different athletes to run 800 metres before and after this training are shown below. $$\begin{array}{l}
\begin{array} {| l | llllllll l| }
\hline \text { }&A&B&C&D&E&F&G&H&I\
\hline \text { Time before training (seconds)}&115.2&120.9&108.0&112.4&107.5&119.1&121.3&110.8&122.3\
\hline \text {Time after training (seconds) }&116.0&119.1&105.1&111.9&109.1&115.2&118.5&110.7&120.9\\hline
\end{array}
\end{array}$$ Construct a 99% confidence interval for the mean difference of the "before" minus "after" times if $\overline { \mathrm { d } } ( \text { before } - \text { after } ) = 1.222 \text { and } \mathrm { s } _ { \mathrm { d } } = 1.826$ .
A)(-0.54,2.98)
B)(-6.42,8.87)
C)(-0.85,3.29)
D)(-0.76,3.20)
E)(-0.82,3.26)

Question

A coach uses a new technique in training middle distance runners.The times for 9 different athletes to run 800 metres before and after this training are shown below. $$\begin{array}{l}
\begin{array} {| l | llllllll l| } 
\hline \text { }&A&B&C&D&E&F&G&H&I\
\hline \text { Time before training (seconds)}&115.2&120.9&108.0&112.4&107.5&119.1&121.3&110.8&122.3\
\hline \text {Time after training (seconds) }&116.0&119.1&105.1&111.9&109.1&115.2&118.5&110.7&120.9\\hline 
\end{array}
\end{array}$$ Construct a 99% confidence interval for the mean difference of the "before" minus "after" times if $\overline { \mathrm { d } } ( \text { before } - \text { after } ) = 1.222 \text { and } \mathrm { s } _ { \mathrm { d } } = 1.826$ .
A)(-0.54,2.98)
B)(-6.42,8.87)
C)(-0.85,3.29)
D)(-0.76,3.20)
E)(-0.82,3.26)

Quizplus · Accepted Answer

The 99% confidence interval for the mean difference is calculated using the formula: $\overline{d} \pm t^* \frac{s_d}{\sqrt{n}}$, where $t^*$ is the t-value for 99% confidence with $n-1$ degrees of freedom. For $n=9$, $t^*\approx 3.355$. Plugging in the values: $1.222 \pm 3.355 \times \frac{1.826}{\sqrt{9}}$, which results in the interval (-0.82, 3.26).

A Coach Uses a New Technique in Training Middle Distance