Chapter PVI, Problem 7RE

(a)

To determine

To explain is there evidence that ALS is more common among athletes.

Answer to Problem 7RE

Yes, there is evidence that ALS is more common among athletes.

Explanation of Solution

It is given in the question that ever since Lou Gehrig developed amyotrophic lateral sclerosis (ALS), this deadly condition has been commonly known as Lou Gehrig's disease. Thus, to do the mechanics of a hypothesis test for equality of population proportions we will use the calculator $\text{TI}-89$ . Then select $6:2-$ PropZTestfrom the STAT Tests menu. Enter the observed counts and sample sizes. Indicate what kind of test you want: one-tail upper tail, lower tail, or two-tail. And specify whether results should simply be calculated or displayed with the area corresponding to the P-value of the test shaded. So, the hypothesis is defined as:

  $\begin{array}{l}{H}_0:p_{\text{ALS}}-p_{\text{Other}}=0\\ H_a:p_{\text{ALS}}-p_{\text{Other}}>0\end{array}$

Thus, by using the calculator $\text{TI}-89$ , the test statistics and the P-value is as:

  $\begin{array}{l}z=2.52\\ P=0.0058\end{array}$

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

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

Thus, we conclude that there is a strong evidence that there is a higher proportion of varsity athletes among ALS patients than those with other disorders.

(b)

To determine

To find out what kind of study is this and how does that affect the inference you made in part (a).

Answer to Problem 7RE

This is an observational retrospective study.

Explanation of Solution

It is given in the question that ever since Lou Gehrig developed amyotrophic lateral sclerosis (ALS), this deadly condition has been commonly known as Lou Gehrig's disease. Since in this study the patients enrolled in the study already have the disease or condition before the study has begun then it is an observational retrospective study. And this affect the inference above in part (a) that one must have to assume the patients studied are representative to make the above inference.