DO YOU KNOW HOW?
8. In a survey, customers select Item A or Item B. Item A is selected by 20
males and 10 females. Of 20 customers who select Item B, five are males.
Calculate conditional relative frequencies for Item A and Item B. Is it
reasonable to conclude that a customer who prefers Item B is more likely to
be a female than a male?
CHECK ANSWER
D

Question

08-05-2024
Mathematics

Answered

DO YOU KNOW HOW?
8. In a survey, customers select Item A or Item B. Item A is selected by 20
males and 10 females. Of 20 customers who select Item B, five are males.
Calculate conditional relative frequencies for Item A and Item B. Is it
reasonable to conclude that a customer who prefers Item B is more likely to
be a female than a male?
CHECK ANSWER
D

Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2024-05-08T23:17:38-04:00

Let's calculate the conditional relative frequencies for each gender given the choice of Item A or Item B, and then we'll determine whether a customer who prefers Item B is more likely to be a female than a male.

First, we look at Item A:
- There are 20 males who selected Item A.
- There are 10 females who selected Item A.
- The total number of people who selected Item A is the sum of males and females, which is [tex]\(20 + 10 = 30\)[/tex].

Let's find the conditional relative frequency for males and females who selected Item A:
- The conditional relative frequency for males who selected Item A: [tex]\( \frac{\text{males who selected A}}{\text{total who selected A}} = \frac{20}{30} = \frac{2}{3} \)[/tex] or approximately 0.6667.
- The conditional relative frequency for females who selected Item A: [tex]\( \frac{\text{females who selected A}}{\text{total who selected A}} = \frac{10}{30} = \frac{1}{3} \)[/tex] or approximately 0.3333.

Next, we analyze Item B:
- We know that 5 males selected Item B, and there are 20 customers in total who selected Item B.
- To find the number of females, we subtract the number of males from the total number: [tex]\(20 - 5 = 15\)[/tex] females selected Item B.

Let's calculate the conditional relative frequency for males and females who selected Item B:
- The conditional relative frequency for males who selected Item B: [tex]\( \frac{\text{males who selected B}}{\text{customers who selected B}} = \frac{5}{20} = \frac{1}{4} \)[/tex] or 0.25.
- The conditional relative frequency for females who selected Item B: [tex]\( \frac{\text{females who selected B}}{\text{customers who selected B}} = \frac{15}{20} = \frac{3}{4} \)[/tex] or 0.75.

Finally, we'll determine if a customer who prefers Item B is more likely to be a female:
- The relative frequency for females who selected Item B is 0.75, and the relative frequency for males who selected Item B is 0.25.
- Since 0.75 (female frequency) is greater than 0.25 (male frequency) for Item B, it is reasonable to conclude that a customer who prefers Item B is more likely to be a female than a male.