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 n

Two-way tables
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asked 2021-06-30

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:

\(\text{Soccer level} \\ \begin{array}{ll|c|c|c} & & \text { Ellte } & \text { Non-elite } & \text { Did not play } \\ \hline \text { Whether person } & \text { Yes } & 10 & 9 & 24 \\ \hline \text { developed arthritis } & \text { No } & 61 & 206 & 548 \end{array}\)

What percent of the elite soccer players developed arthritis? What percent of those who got arthritis were elite soccer players?

Answers (1)

2021-07-01
We note that 10 players were elite players with arthritis and 61 players were elite players with arthritis. The percent of elite players who have arthritis is then the total number of elite players with arthritis divided by the number of elite players:
\(\displaystyle\frac{{10}}{{{10}+{61}}}=\frac{{10}}{{71}}\sim{0.1408}={14.08}\%\)
We note that 10 players were elite players with arthritis, 9 players were non-elite players with arthritis and 24 players with arthritis did not play.
The percent of people with arthritis that were elite players is then the total number of elite players with arthritis divided by the number of people with arthritis:
\(\displaystyle\frac{{10}}{{{10}+{9}+{24}}}=\frac{{10}}{{43}}\sim{0.2326}={23.26}\%\)
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