Q 77. - The Practice of Statistics for AP

Question

A study in Sweden looked at former elite soccer players, people who had played soccer but not at the elite level, and people of the same age who did not play soccer. Here is a two-way table that classifies these individuals by whether or not they had arthritis of the hip or knee by their mid-fifties: 

(a) What percent of the people in this study were elite soccer players? What percent had arthritis? 

(b) What percent of the elite soccer players had arthritis? What percent of those who had arthritis were elite soccer players? 

Step-by-Step Solution

Answer

Part (a) $8.28\%$ and $5.01\%$ respectively.

Part (b) $23.26\%$  elite players and $14.08\%$  elite soccer players.

Part (a) Step 1: Given information

Given table : 

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

Part (a) 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

Part (a) Step 3: Explanation

The two-way tables demonstrate the dangers of playing soccer for individuals based on whe10ther or not they had arthritic hips or knees by the time they were in their fifties. 

	Arthritis	No arthritis	Total
Elite	10	61	71
No elite	9	206	215
Did not play	24	548	572
Total	43	815	858

Individuals who were elite players, no-elite players and those who did not play soccer were classified in a two-way table.

$$\begin{gathered} =\frac{total number of elite soccer players}{total number of soccer players} \\ = 71/858 \end{gathered}$$

Number of professional soccer players=$$\begin{gathered} = 0.082751 \\ = 0.0828 \\ = 8.28\% \end{gathered}$$

$= \frac{total number of arthritis}{total number of soccer players}$

Proportion of arthritis $$\begin{gathered} =\frac{43}{858} \\ =0.050117 \\ =5.01\% \end{gathered}$$

As a result, the percentages of elite soccer players with arthritis are $8.28$ percent and $5.01$ percent, respectively.

Part (b) Step 1: Explanation

The percentage of elite soccer players who had arthritis was high. 

$$\begin{gathered} \left(proportion of arthritis were elite soccer players\right)=\frac{\left(total number of arthritis were elite soccer players\right)}{\left(total number of arthritis\right)} \\ = 10 43 \\ = 0.2326 \\ = 23.26\% \end{gathered}$$

Elite soccer players have the highest rate of arthritis.

As a result, $23.26$ percent of those with arthritis were top soccer players, and $14.08$ percent of those with arthritis were elite soccer players.