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

Answer:

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

Step-by-step explanation:

The relative frequency for a data set n is calculated by dividing each frequency $f_{x_i}$ by n

$f_r = \frac{f_{x_i}}{n}$.

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

-------------------------------------------------- --------------------------------------

  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. $f_r = \frac{12}{17} = 0.705$

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

-------------------------------------------------- ----------------------------------------------------------

 Sport           No Sport      Total n

  9                       4                 13

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

-------------------------------------------------- --------------------------------------

 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. $f_r = \frac{9}{13} = 0.69$

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.