Chapter 24, Problem 19E

(b)

To determine

To interpret your interval.

Explanation of Solution

In the question, the average numbers of runs scored in American league and National league games are recorded. Thus, we have,

  $\begin{array}{l}{\overline{x}}_1=9.854\\ {\overline{x}}_2=9.4375\\ n_1=13\\ n_2=16\\ s_1=0.566\\ s_2=0.408\\ \alpha =0.05\end{array}$

The confidence interval is $(-0.18,0.89)$ . Thus, we interpret from this that we are $95\%$ confident that American league games average between $(-0.18,0.89)$ more per game than the National league game.

(c)

To determine

To explain does the interval suggest that the two leagues may differ in average number of runs scored per game.

Answer to Problem 19E

No, it does not.

Explanation of Solution

In the question, the average numbers of runs scored in American league and National league games are recorded. Thus, we have,

  $\begin{array}{l}{\overline{x}}_1=9.854\\ {\overline{x}}_2=9.4375\\ n_1=13\\ n_2=16\\ s_1=0.566\\ s_2=0.408\\ \alpha =0.05\end{array}$

Thus, the interval does not suggest that the two leagues may differ in average number of runs scored per game because the confidence interval contain zero. So, if in the confidence interval contain zero in it then two league does not differ.