Question

Cooling Down. Refer to Exercise 10.128 and find a $98\%$ confidence interval for the difference between the mean times to fatigue on a treadmill in a hot and humid environment after cooling down with cold water and after cooling down with an ice slurry.

Short answer

The data has a $98\%$ confidence interval of $(-7.33,-4.47)$.

Step-by-step solution

Given Information

The given data is,

$\begin{array}{|ccc|}\hline \text{Subject}& \text{Cold water}& \text{Ice slurry}\\ 1& 52& 56\\ 2& 37& 43\\ 3& 44& 52\\ 4& 51& 58\\ 5& 34& 38\\ 6& 38& 45\\ 7& 41& 45\\ 8& 50& 58\\ 10& 38& 44\\ \hline\end{array}$

Explanation

The null and alternative hypotheses are,

$H_0:{\mu }_d=0$

$H_a:{\mu }_d<0$

The output of MINITAB is presented below.

$-11.70,0$are the test statistics and $p$values.

Explanation

Level of significance has a critical value of $2.821$.

The confidence level is,

$CI=\overline{d}\pm t_{\frac{a}{2}}\frac{s_d}{\sqrt{n}}$

$=-5.9\pm (2.821)\frac{1.6}{\sqrt{10}}$

$=(-7.33,-4.47)$