A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A,B,and C.The consumers are classified according to age and package design preference.
Are "B" and "25 or older" independent and why or why not?
A)No,because P (25 or over |
B)$\neq$ P (
B)Yes,because P (
B)= P(
C)No,because P (25 or older |
B)$\neq$ P (25 or older)
D)Yes,because P (25 or older $\cap$
B)$\neq$ 0
E)No,because age and package design are different things

Question

A market research firm is investigating the appeal of three package designs.The table below gives information obtained through a sample of 200 consumers.The three package designs are labeled A,B,and C.The consumers are classified according to age and package design preference. 
 Are "B" and "25 or older" independent and why or why not?
A)No,because P (25 or over | 
B)$\neq$ P (
B)Yes,because P (
B)= P(
C)No,because P (25 or older | 
B)$\neq$ P (25 or older) 
D)Yes,because P (25 or older $\cap$ 
B)$\neq$ 0 
E)No,because age and package design are different things

Quizplus · Accepted Answer

The independence between "B" and "25 or older" can be tested using the formula P(B and 25 or older) = P(B) * P(25 or older). If the formula holds true, then "B" and "25 or older" are independent. However, based on the given information, the values for P(25 or older | B) and P(25 or older) are different, which means the formula does not hold true. Therefore, "B" and "25 or older" are not independent. The correct choice is C.

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