Chapter 1.2, Problem 86E

(a)

To determine

To find: the percent of the people in the study were elite soccer players and the people in this study developed arthritis.

Answer to Problem 86E

Elite: 8.275%

Arthritis: 5.01%

Explanation of Solution

Given:

Soccer level
		Elite	Non-Elite	Did not play
Whether person	Yes	10	9	24
Developed arthritis	No	61	206	548

Calculation:

By seeing the table, it is observed that 10 players were elite players with arthritis and 61 players were elite players with arthritis.

The required percent is

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

It is also observed 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 required percents are

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

(b)

To determine

To find: the elite soccer players develop arthritis and of those who got arthritis were elite soccer players.

Answer to Problem 86E

Elite with arthritis: 14.08%

People with arthritis who are elite players: 23.26%

Explanation of Solution

Given:

Soccer level
		Elite	Non-Elite	Did not play
Whether person	Yes	10	9	24
Developed arthritis	No	61	206	548

Calculation:

By seeing the table, it is observed that 10 players were elite players with arthritis and 61 players were elite players with arthritis.

The required percentage is

  $\frac{10}{10+61}=\frac{10}{71}=0.1408=14.08\%$

By seeing the table, it is observed 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 required percentage is

  $\frac{10}{10+9+24}=\frac{10}{43}=0.2326=23.26\%$

(c)

To determine

To Explain: the confirmation about the suspicion and calculate the appropriate percentage to help the answer.

Answer to Problem 86E

Yes

Explanation of Solution

Given:

Soccer level
		Elite	Non-Elite	Did not play
Whether person	Yes	10	9	24
Developed arthritis	No	61	206	548

Calculation:

By seeing the table it is observed that the 10 players were elite players with arthritis and 61 players were elite players with arthritis.

The required percentage is

Percent of elite players who have arthritis = $\frac{10}{10+61}=\frac{10}{71}=0.1408=14.08\%$

By seeing the table it is observed 9 players were non-elite players with arthritis and 206 players were non-elite players with arthritis.

The required percentage is

Percent of non-elite players who have arthritis = $\frac{9}{9+206}=\frac{9}{215}=0.04186=4.186\%$

It is observed that the percent of elite players who have arthritis (14.08%) is too much higher than the percent of non-elite players who have arthritis (4.186%), which verify the suspicion, that the more serious soccer players (elite players) were more likely to develop arthritis later in life.