Chapter 24, Problem 20E

(a)

To determine

To test appropriate hypotheses and state your conclusion.

Explanation of Solution

In the question, the mortality rate and the derby of north and south data is collected for both and the box plot for the same is given. It is also given that:

  $\begin{array}{l}{\overline{x}}_1=1631.59\\ {\overline{x}}_2=1388.85\\ n_1=34\\ n_2=27\\ s_1=138.470\\ s_2=151.114\end{array}$

Now, let us define the hypotheses for testing:

  $\begin{array}{l}{H}_0:{\mu }_1={\mu }_2\\ H_1:{\mu }_1\ne {\mu }_2\end{array}$

Thus, the value of test statistic is:

  $\begin{array}{l}t=\frac{{\overline{x}}_1-{\overline{x}}_2}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\\ =\frac{1631.59-1388.85}{\sqrt{\frac{{138.470}^2}{34}+\frac{{151.114}^2}{27}}}\\ =6.47\end{array}$

And the degrees of freedom is:

  $\begin{array}{l}df=\frac{(\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2})}{\frac{{(\raisebox{1ex}{$s_1^2$}\!\left/ \!\raisebox{-1ex}{$n_1$}\right.)}^2}{n_1-1}+\frac{{(\raisebox{1ex}{$s_2^2$}\!\left/ \!\raisebox{-1ex}{$n_2$}\right.)}^2}{n_2-1}}\\ =53\end{array}$

Therefore, the P-value will be:

  $P<0.01$

As we know that if the P-value is less than or equal to the significance level, then the null hypothesis is rejected. So,

  $P<0.05\Rightarrow \text{Reject }{H}_0$

Thus, we conclude that there is a sufficient evidence to support the claim of a difference.

(b)

To determine

To explain what effect might the outlier have had on your test.

Explanation of Solution

In the question, the mortality rate and the derby of north and south data is collected for both and the box plot for the same is given. And there is a sufficient evidence to support the claim of a difference. So, the outlier might have had effect on our test that the large outlier would have increased both the mean and the standard deviation of the North group, which could then exaggerate the actual differences between the two groups and thus it is possible that there actually is no significant difference (if the outlier is not taken into account).