Question

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.

• column: in a band, play a sport; row: not in a band, do not play a sport
• column: not in a band, play a sport; row: in a band, do not play a sport
• column: in a band, do not play a sport; row: not in a band, play a sport
• column: in a band, not in a band; row: play a sport, do not play a sport

Explanation:

To solve this, we analyze the categories: band participation (in band, not in band) and sport participation (play sport, do not play sport). A two - way table (contingency table) typically has one variable for columns and one for rows. Here, band participation (in band, not in band) can be columns and sport participation (play sport, do not play sport) can be rows (or vice - versa). Let's check the options:

• Option 1: Columns are "In a Band, Play a Sport" (mixes band and sport) and rows are "Not in a Band, Do Not Play a Sport" (mixes), so incorrect.
• Option 2: Columns are "Not in a Band, Play a Sport" (mixes) and rows are "In a Band, Do Not Play a Sport" (mixes), incorrect.
• Option 3: Columns are "In a Band, Do Not Play a Sport" (mixes) and rows are "Not in a Band, Play a Sport" (mixes), incorrect.
• Option 4: Columns are "In a Band, Not in a Band" (band participation) and rows are "Play a Sport, Do Not Play a Sport" (sport participation), which is the correct way to set up a two - way table for this data.

Answer:

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