Chapter 12.1, Problem 32E

To determine

To explain do these data provide convincing evidence of an association between environmental club membership and snowmobile use for the population of visitors to Yellowstone National park.

Answer to Problem 32E

Yes, these data provide convincing evidence of an association between environmental club membership and snowmobile use for the population of visitors to Yellowstone National park.

Explanation of Solution

The table of the environmental clubs member and non-members are given with the numbers of person who have never used snowmobile, are snowmobiles renter, are snowmobile owners are given. Thus, we want to test for an association between the two categorical variables which is done by using a chi-square test. Thus, we have,

  

The value of test statistics is then,

  $\begin{array}{l}{\chi }^2=\frac{{(445-525.6861)}^2}{525.6861}+\frac{{(212-131.3139)}^2}{131.3139}+\frac{{(497-459.2752)}^2}{459.2752}+\frac{{(77-114.7248)}^2}{114.7248}\\ +\frac{{(279-236.0387)}^2}{236.0387}+\frac{{(16-58.9613)}^2}{58.9613}\\ =116.588\end{array}$

The degrees of freedom is then,

  $\begin{array}{l}df=(r-1)(c-1)\\ =(3-1)(2-1)\\ =2\end{array}$

Thus, the P-value is,

  $P<0.0005$

Therefore, we have that,

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

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