Question

Researchers suspected that the more serious soccer players were more likely to develop arthritis later in life. Do the data confirm this suspicion?

Two-way tables
ANSWERED
asked 2021-08-11

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

Expert Answers (1)

2021-08-12
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:
Percent of elite players who have arthritis \(\displaystyle=\frac{{10}}{{{10}+{61}}}=\frac{{10}}{{71}}\sim{0.1408}={14.08}\%\)
We note that 9 players were non-elite players with arthritis and 206 players were non-clite players with arthritis.
Percent of elite players who have arthritis =
The percent of non-elite players who have arthritis is then the total number of non-elite players with arthritis divided by the number of non-clite players:
We then note that the percent of elite players who have arthritis (14.08%) is much higher than the percent of non-elite players who have arthritis (4.186%), which confirms the suspicion that the more serious soccer players were more likely to develop arthritis later in life.
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