Chapter 1.2, Problem 78E

To determine

To find: whether there is an association between elite soccer and developing arthritis or not

Answer to Problem 78E

It appears that there is an association between elite soccer and developing arthritis.

Explanation of Solution

Given:

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

Calculation:

Given:

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

Let us first determine the row and column totals of the given table:

	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	$10+61=71$	$9+206=215$	$24+548=572$	$43+815=858$

Determine the proportion of people with arthritis or no arthritis for each category of player, by dividing every number in the table by its column total.

	Elite	Non-Elite	Did not play
Arthritis	$\frac{10}{71}\approx 0.1408$	$\frac{9}{215}\approx 0.0419$	$\frac{24}{572}\approx 0.0420$
No arthritis	$\frac{61}{71}\approx 0.8592$	$\frac{206}{215}\approx 0.9581$	$\frac{548}{572}\approx 0.9580$

Bar graph

The width of each bar has to be the same and the height has to be equal to the proportion in the previous table:

  

We note that the proportion of 0.1408 for elite players with arthritis is a lot higher than the proportion of players with arthritis in the other categories (0.0419/0.0420).

Thus it appears that there is an association between elite soccer and developing arthritis.

Conclusion:

Thus it appears that there is an association between elite soccer and developing arthritis.