Question

Risks of playing soccer (1.1) 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:

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

Part (b). What percent of the elite soccer players developed arthritis? What percent of those who got arthritis were elite soccer players?

Part (c). Researchers suspected that the more serious soccer players were more likely to develop arthritis later in life. Do the data confirm this suspicion? Calculate appropriate percentages to support your answer.

Short answer

Part (a)

Elite = 8.275%

Arthritis = 5.01%

Part (b)

Elite with Arthritis = 14.08%

People with arthritis who are elite player = 23.26%

Part (c) Yes

Step-by-step solution

Part (a). Step 1. Given information. 

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

Part (a). Step 2. What proportion of the participants in this study were elite soccer players? How many people in this study developed arthritis?

We can see that 10 players were elite players with arthritis, while 61 were elite players with arthritis.

The percentage of people who were elite players is then calculated by dividing the total number of elite players by the sample size:

$$\begin{gathered} \frac{10+61}{10+61+9+206+24+548}=\frac{71}{858} \\ \frac{71}{858}\approx 0.08275 \\ 0.08275=8.275\% \end{gathered}$$

We note that 10 players with arthritis were elite players, 9 were non-elite players, and 24 players with arthritis did not play.

The percentage of people with arthritis is then calculated by dividing the total number of players with arthritis by the sample size:

$$\begin{gathered} \frac{10+9+24}{10+61+9+206+24+548}=\frac{43}{858} \\ \frac{43}{858}\approx 0.0501 \\ 0.0501=5.01\% \end{gathered}$$

Part (b). Step 1. How many elite soccer players developed arthritis? How many of those who developed arthritis were elite soccer players?

We can see that 10 players were elite players with arthritis, while 61 were elite players with arthritis.

The percent of elite players with arthritis is calculated by dividing the total number of elite players with arthritis by the total number of elite players.

$$\begin{gathered} \frac{10}{10+61}=\frac{10}{71} \\ \frac{10}{71}\approx 0.1408 \\ 0.1408=14.08\% \end{gathered}$$

We note that 10 players with arthritis were elite players, 9 were non-elite players, and 24 players with arthritis did not play.

The percentage of people with arthritis who were elite players is then calculated by dividing the total number of elite players with arthritis by the total number of people with arthritis:

$$\begin{gathered} \frac{10}{10+9+24}=\frac{10}{43} \\ \frac{10}{43}\approx 0.2326 \\ 2326=23.26\% \end{gathered}$$

Part (c). Step 1. Yes Researchers suspected that more serious soccer players had a higher risk of developing arthritis later in life.

We can see that 10 players were elite players with arthritis, while 61 were elite players with arthritis.

The percent of elite players with arthritis is then calculated by dividing the total number of elite players with arthritis by the total number of elite players:

The percentage of elite players who suffer from arthritis

$$\begin{gathered} \frac{10}{10+61}=\frac{10}{71} \\ \frac{10}{71}\approx 0.1408 \\ 0.1408=14.08\% \end{gathered}$$

We can see that there were 9 non-elite players with arthritis and 206 non-elite players with arthritis.

The percent of non-elite players with arthritis is calculated by dividing the total number of non-elite players with arthritis by the total number of non-elite players:

Percent of non-elite players who suffer from arthritis

$$\begin{gathered} \frac{9}{9+206}=\frac{9}{215} \\ \frac{9}{215}\approx 0.04186 \\ 0.04186=4.186\% \end{gathered}$$

The percentage of elite players with arthritis (14.08 percent) is much higher than the percentage of non-elite players with arthritis (4.186 percent), confirming the suspicion that the more serious soccer players (elite players) were more likely to develop arthritis later in life.

As a result:

Yes