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Question

Problem #1:

100 adults and 100 teenagers were polled and asked if they liked the food choices found in the local food court at the mall.  21 of the adults liked the food court choices, and 96 of the teenagers liked the food court choices.

a) Make a two-way table for this data that shows the joint and marginal frequencies.

b) Make a two-way table that shows the joint and marginal relative frequencies.

c) Make a two-way table that shows the conditional relative frequencies based on the column totals.

d) What conclusions can you draw based on your results? Explain.

Answer 1

The tables went a bit wonky once submitted.

a) The two way table is a tool used to show how many respondents (in this case adults and teenagers) picked a given response to the question (liked or disliked the food court choices)

Liked Disliked Joint Frequencies

Adults 21 79 100

Teenagers 96 4 100

Joint Frequencies 117 83

b) Similar to problem (a) but requires RELATIVE frequency, since there is no condition it is assumed to be relative to the entire population (100 adults + 100 teenagers = 200 people)

Liked Disliked Joint Frequencies

Adults 21/200 ≅ .11 or 11% 79/200 ≅ .40 or 40% 100/200 = .5 or 50%

Teenagers 96/200 = .48 or 48% 4/200 = .02 or 2% 100/200 = .5 or 50%

Joint Frequencies 117/200 ≅ .59 or 59% 83/200 ≅ .42 or 42%

c) Similar to problem (b) but is conditional on the column totals (how many people liked [21+96=117] or disliked [79+4=83])

Liked Disliked

Adults 21/117 ≅ .18 or 18% 79/83 ≅ .95 or 95%

Teenagers 96/117 ≅ .82 or 82% 4/83 = .05 or 5%

d) Teenagers account for 82% of respondents who like food court choices, while 95% of respondents who don't like the food court choices were adults. From problem (b) we can see that 59% of respondents like the current offerings at the food court.