Question

Snowmobiles (11.2) 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? Carry out an appropriate test at the $5\%$ significance level

Short answer

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.

Step-by-step solution

Given Information

Explanation

The numbers of those who have never used a snowmobile, are snowmobile renters, and are snowmobile owners are shown in a table of environmental club members and non-members. As a result, we'll use a chi-square test to see if there's a link between the two categorical variables. Thus

Explanation

The value of test statistics is then,

${\chi }^2=\frac{(445-525.6861{)}^2}{525.6861}+\frac{(212-131.3139{)}^2}{131.3139}+\frac{(497-459.2752{)}^2}{459.2752}+\frac{(77-114.7248{)}^2}{114.7248}$ $=116.588$

The degrees of freedom is then,

$df=(r-1)(c-1)$

$=(3-1)(2-1)$

$=2$

Thus, the P-value is,

$P<0.0005$

Therefore, we have that,

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

As a result, we conclude that the claim of association is supported by sufficient evidence.