Chapter PVI, Problem 12RE

To determine

To create a $95\%$ confidence interval for the difference in driver deaths rates for the two types of vehicles and explain are these data appropriate for this inference.

Answer to Problem 12RE

The confidence interval is $(-30.976,21.976)$ and the data is appropriate.

Explanation of Solution

It is given in the question that a study of auto safety determined the number of driver per million vehicle sales, classified by type of vehicles. Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $4:2-$ SampTInt. You must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify the desired level of confidence. So, we have,

Midsize	SUV
47	55
54	60
64	62
76	76
88	91
97	109

And $\alpha =0.05$ so by using the calculator $\text{TI}-89$ , we have,

  $\begin{array}{l}P=0.7095\\ \text{Margin of error}=26.476\end{array}$

And the confidence interval is:

  $(-30.976,21.976)$ .

Thus, we are $95\%$ confident the difference in driver deaths rates for the two types of vehicles lie between $(-30.976,21.976)$ . And since the interval contains zero in it then the data is appropriate for the inference.