Q 25. - The Practice of Statistics for AP

Question

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.

Step-by-Step Solution

Answer

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 1: 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

Step 2: 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. 

Step 3: 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	$\frac{212}{305}\times 100$	69.5
Snowmobile	77	$\frac{77}{350}\times 100$	25.3
Snowmobile owner	16	$\frac{16}{305}\times 100$	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	$\frac{445}{1221}\times 100$	36.4
Snowmobile	497	$\frac{497}{1221}\times 100$	40.7
Snowmobile owner	279	$\frac{279}{1221}\times 100$	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	$\frac{212}{305}\times 100$	69.5%	$\frac{445}{1221}\times 100$	36.4%
Snowmobile	$\frac{77}{305}\times 100$	25.3%	$\frac{497}{1221}\times 100$	40.7%
Snowmobile owner	$\frac{16}{305}\times 100$	5.2%	$\frac{279}{1221}\times 100$	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.