Question

A teacher collected data from a class of eighth grade students on whether or not they play a sport and whether or not they are in the school musical. The two-way table below shows the data collected.

Which association does the two-way table suggest?
A. None of the associations listed are correct.

B. Those who are in the school musical tend not to play a sport.

C. Those who are in the school musical tend to play a sport.

D. Those who are not in the school musical tend not to play a sport.

Answer 1

B. Those who are in the school musical tend not to play a sport.

Explanation:

The relative frequency for a data set n is calculated by dividing each frequency
`f_(x_i)` by n

`f_r = (f_(x_i))/(n)`.

We have a table that relates students who are in music school with students who practice a sport.

First, we take the population that is in the music school from the table.

Then, of the students who are in the music school, 5 practice some sport and 12 do not practice any sport

Then we calculate the relative frequencies for those who practice a sport and those who do not practice any sport.

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Relative frequency Students that are in the school musical. n=17.

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Sport No Sport Total n

5 12 17

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Relative frequency Students that are in the school musical. n=17

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Sport (fr) No Sport (fr) Total n

5/17 = 0.29 12/17= 0.71 17

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Most students who are in music school do not practice a sport.
`f_r = (12)/(17) = 0.705`

70% of students who are in music school do not practice a sport

Now we calculate the relative frequency of students who are not in music school. Of these students 9 of them practice a sport and 4 of them do not practice any sport.

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Relative frequency Students that are not in the school musical. n=13

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Sport No Sport Total n

9 4 13

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Relative frequency Students that are not in the school musical. n=13

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Sport (fr) No Sport (fr) Total n

9/13= 0.69 4/13= 0.21 13

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Note that of students who are not in music school, most of them practice a sport.
`f_r = (9)/(13) = 0.69`

Finally you can conclude that the association does the two-way table suggest is:

B. Those who are in the school musical tend not to play a sport.