Q 25. Snowmobiles in the park Yellowst... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 1: Q 25. (page 25)

Snowmobiles in the park Yellowstone National Park surveyed a random sample of $1526$ winter visitors to the park. They asked each person whether they owned, rented, or had never used a snowmobile. Respondents were also asked whether they belonged to an environmental organization (like the Sierra Club). The two-way table summarizes the survey responses.
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? Follow the four-step process.

Short Answer

Expert verified

Around $70$ percent of environment club members are people who have never used the snowmobile only around 5 percent of Environment club members are snowmobile owners. Snowmobile rentals make up roughly $41 %$ of non-members of the Environment Club.

Step by step solution

Given Information

The information on environmental clubs is shown in the below table which was got from two-way table survey responses:

	Environmental clubs
	No	Yes	total
Never used	445	212	657
Snowmobile	497	77	574
Snowmobile owner	279	16	295
Total	1221	305	1526

Concept

The distribution of a category variable is displayed using pie charts and bar graphs. Any set of quantities measured in the same units can be compared using bar graphs. It's a good idea to ask yourself, "What do I see?" when looking at any graph.

Explanation

The following is a conditional distribution of now mobile use by winter visitors to Yellowstone National Park to members of the environment club:

Conditional distribution of snow mobile use of environmental club members
Snow mobile use	Member of environmental club	Percentage
Never used	212	$\frac{212}{305} 脳 100$	69.5
Snowmobile	77	$\frac{77}{350} 脳 100$	25.3
Snowmobile owner	16	$\frac{16}{305} 脳 100$	5.2
Total	305		100

The conditional distribution of snowmobile use by winter visitors to Yellowstone National Park among non-members of environmental clubs is shown below.

Conditional distribution of snow mobile use of environmental club Non- members
Snow mobile use	Member of environmental club	Percentage
Never used	445	$\frac{445}{1221} 脳 100$	36.4
Snowmobile	497	$\frac{497}{1221} 脳 100$	40.7
Snowmobile owner	279	$\frac{279}{1221} 脳 100$	22.9
Total	1221		100

The following is a conditional distribution comparison table:

Conditional distribution of snow mobile use of environmental club member and Non- members
Snow mobile use	environmental club member	Non- members of environmental club	Percentage
Never used	$\frac{212}{305} 脳 100$	69.5%	$\frac{445}{1221} 脳 100$	36.4%
Snowmobile	$\frac{77}{305} 脳 100$	25.3%	$\frac{497}{1221} 脳 100$	40.7%
Snowmobile owner	$\frac{16}{305} 脳 100$	5.2%	$\frac{279}{1221} 脳 100$	22.9%
Total		100%		100%

Step III-Achieve: We'll create a side-by-side bar graph to compare the perspectives of environmental club members and non-members:

Step IV-CONCLUDE: As a result, about $70 %$ of environment club members have never used a snowmobile ( $69.5$ percent vs $36.4 %$ ), and only about $5 %$ of environment club members possess a snowmobile ( $5.2$ percent vs $22.9$ percent ). Snowmobile rentals make up roughly $41 %$ of non-members of the Environment Club ( $25.3$ percent vs $40.7$ percent ).

As a result, over $70 %$ of environment club members have never used a snowmobile, whereas only about $5 %$ of environment club members possess a snowmobile. Snowmobile rentals make up roughly $41 %$ of non-members of the Environment Club.