Q 78. - The Practice of Statistics for AP

Question

Refer to Exercise $77$. We suspect that the more serious soccer players have more arthritis later in life. Do the data confirm this suspicion? Give graphical and numerical evidence to support your answer. 

Step-by-Step Solution

Answer

There appears to be a link between top soccer and the development of arthritis.

Step 1: Given Information

Given: 

	Elite	Non elite	Did not play
Arthritis	10	9	24
No Arthritis	61	206	548

Step 2: Concept

When objects need to be displayed in a way that demonstrates the hierarchical structure as well as amount or size, pyramid charts are the ideal choice. This can include positions in management, items sold, and business locations, among other things.

Step 3: Explanation

Let's start by calculating the table's row and column totals: 

	Elite	Non-elite	Did not play	Total
Arthritis	10	9	24	10+9+24=43
No arthritis	61	206	548	61+206+548=815
Total	10+61=71	9+206=215	24+548=572	43+815

Divide each number in the table by its column total to find the proportion of people with arthritis or no arthritis for each player group. 

	Elite	Non elite	Did not play
Arthritis	10/71=0.1408	9/215=0.0419	24/572=0.0420
No arthritis	61/71=0.8592	206/215=0.9581	548/572=0.9580

Graph with bars

Each bar's width must be the same, and its height must be the same as the proportion in the previous table: 

The percentage of elite players with arthritis $(0.1408)$ is significantly greater than the percentage of players with arthritis in the other categories $(0.0419/0.0420)$ As a result, it appears that top soccer and the development of arthritis are linked.