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Chapter 12: Q.32 (page 765)

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

Expert verified

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

01

Given Information

02

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

03

Explanation

The value of test statistics is then,

χ2=(445-525.6861)2525.6861+(212-131.3139)2131.3139+(497-459.2752)2459.2752+(77-114.7248)2114.7248 =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⇒RejectH0

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

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