A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. Choose a possible description for the rows and columns.

D) Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

Explanation:

The answer choices are:

A) Column: In a Band, Play a Sport; Row: Not in a Band, Do Not Play a Sport B) Column: Not in a Band, Play a Sport; Row: In a Band, Do Not Play a Sport C) Column: In a Band, Do Not Play a Sport; Row: Not in a Band, Play a Sport D) Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

Solution

You should build a two-way frequency table with:

Play in the band, and not play in the band Play a sport, and do not play a sport.

It is not important if playing/not playing in the band are in columns or in rows; the important thing is they both must below either to different columns or to different rows. The same is valid for playing a sport.

Then, these two forms are good for the two-way frequency table:

Option 1:

Play in the band Do not play in the band Total

Play sport

Do not play sport

Total

Option 2:

Play sport Do not play sport Total

Play in the band

Do not play in the band

Total

As for the options:

A) Column: In a Band, Play a Sport; Row: Not in a Band, Do Not Play a Sport

This is placing In a band and Play a sport in different columns, when they should be in different rows,

B) Column: Not in a Band, Play a Sport; Row: In a Band, Do Not Play a Sport

This is placing not in a band and Play a Sport in different columns when they should be in different rows.

C) Column: In a Band, Do Not Play a Sport; Row: Not in a Band, Play a Sport

This is placing In a band and Do not play a Sport in different columns when they should be in different rows.

D) Column: In a Band, Not in a Band; Row: Play a Sport, Do Not Play a Sport

This correctly describes the survey: it corresponds to the option #1 above.