Chapter 1.2, Problem 77E

(a)

To determine

To find: the percent of the people who are elite soccer players and having arthritis

Answer to Problem 77E

8.28% and 5.01% respectively.

Explanation of Solution

Given:

  

Calculation:

The two-way tables shows the risks playing soccer individuals by whether or not they had arthritis of the hip or knee by their mind-fifties.

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

In a two way table classifying the individuals who were elite players, no-elite players and those who did not play soccer.

Proportion of elite soccer players $\begin{array}{l}=\frac{\text{total number of elite soccer players}}{\text{total number of soccer players}}\\ =\frac{71}{858}\\ =0.082751\\ =0.0828\\ =8.28\%\end{array}$

Proportion of arthritis $\begin{array}{l}=\frac{\text{total number of arthritis}}{\text{total number of soccer players}}\\ =\frac{43}{858}\\ =0.050117\\ =5.01\%\end{array}$

Conclusion:

“Therefore, the percent of the people who are elite soccer players and having arthritis is 8.28% and 5.01% respectively.”

(b)

To determine

To find: the percent of the elite soccer players having arthritis and arthritis people who are elite soccer players.

Answer to Problem 77E

23.26% elite players and 14.08%elite soccer players.

Explanation of Solution

Calculation:

The proportion of elite soccer players had arthritis,

  $\begin{array}{l}\left(\begin{array}{l}\text{proportion of elite soccer}\\ \text{players had arthritis}\end{array}\right)=\frac{\left(\begin{array}{l}\text{total number of elite soccer}\\ \text{players had arthritis}\end{array}\right)}{\text{total number of soccer players had arthritis}}\\ =\frac{10}{71}\\ =0.140845\\ =14.08\%\end{array}$

The proportion of arthritis were elite soccer players,

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

Conclusion: “Hence, 23.26% of those who had arthritis were elite players and 14.08% of those who are elite soccer players had arthritis.”