Exercise 12 Page 626

	Food Court
Shoppers	Like	Dislike	Total
Adults	0.105	0.395	0.5
Teenagers	0.48	0.02	0.5
Total	0.585	0.415	1

	Food Court
Shoppers	Like	Dislike
Adults	0.21	0.79
Teenagers	0.96	0.04

Practice makes perfect

a Consider the two-way table that shows the results of the survey conducted at the shopping mall.

	Food Court
Shoppers	Like	Dislike
Adults	21	79
Teenagers	96	4

In order to construct the frequency tables, we need to calculate the total values of all the rows in the table.

	Food Court
Shoppers	Like	Dislike	Total
Adults	21	79	21+ 79=100
Teenagers	96	4	96+ 4=100

Similarly, we also need to calculate the total values of all the columns in the table.

	Food Court
Shoppers	Like	Dislike	Total
Adults	21	79	100
Teenagers	96	4	100
Total	21+ 96=117	79+ 4=83	100+ 100=200

We want to use this table to construct a two-way table that shows the joint and marginal relative frequencies. To do so, we will start by dividing each joint frequency by the grand total, 200, to obtain the joint relative frequencies.

	Food Court
Shoppers	Like	Dislike
Adults	21/200 =0.105	79/200 =0.395
Teenagers	96/200 =0.48	4/200 =0.02

Similarly, we will divide each marginal frequency by the grand total to obtain the marginal relative frequencies.

	Food Court
Shoppers	Like	Dislike	Total
Adults	0.105	0.395	100/200 =0.5
Teenagers	0.48	0.02	100/200 =0.5
Total	117/200 =0.585	83/200 =0.415	200/200 =1

b A conditional relative frequency is the ratio of a joint relative frequency to the marginal relative frequency. Consider the two-way frequency table that we constructed in exercise A.

	Food Court
Shoppers	Like	Dislike	Total
Adults	21	79	100
Teenagers	96	4	100
Total	117	83	200

We want to construct a two-way table that shows the conditional relative frequencies based on the totals of the rows. To do so, we will divide each joint frequency by its corresponding row total. For our table we will not have marginal frequencies. Let's do it!

	Food Court
Shoppers	Like	Dislike
Adults	21/100 =0.21	79/100 =0.79
Teenagers	96/100 =0.96	4/100 =0.04

In the context of the exercise, we can say that 21 % of the adults like the new food court and 79 % do not. Additionally, 96 % of the surveyed teenagers answered like and 4 % dislike when asked the same question.

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Exercises p.624-626

Exercise 12 Page 626

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