Chapter PVI, Problem 13RE

(a)

To determine

To create a $95\%$ confidence interval for the difference in mean ages of the two groups.

Answer to Problem 13RE

We are $95\%$ confident that patients with cardiac disease average between $(3.39,5.01)$ years older than those without cardiac disease.

Explanation of Solution

It is given in the question that in a study of how depression may affect one's ability to survive a heart attack, the researchers reported the ages of the two groups they examined. 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,

  $\begin{array}{l}{n}_1=2397\\ {\overline{x}}_1=69.8\\ s_1=8.7\\ n_2=450\\ {\overline{x}}_2=74\\ s_2=7.9\end{array}$

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

  $\begin{array}{l}t=1.966\\ \text{Margin of error}=0.8112\end{array}$

Thus, the confidence interval will be as:

  $(3.39,5.01)$ .

So, we are $95\%$ confident that patients with cardiac disease average between $(3.39,5.01)$ years older than those without cardiac disease.

(b)

To determine

To explain how might an age difference confound these research findings about the relationship between depression and ability to survive a heart attack.

Explanation of Solution

It is given in the question that in a study of how depression may affect one's ability to survive a heart attack, the researchers reported the ages of the two groups they examined. Thus, an age difference confound these research findings about the relationship between depression and ability to survive a heart attack as older people have more chances to have any health issue and older people might also be more likely to be depressed.