51. The research team at a leading perfume company is trying to test the market

Question

51. The research team at a leading perfume company is trying to test the market for its newly introduced perfume. In particular the team wishes to look for gender and international differences in the preference for this perfume. They sample 2,500 people internationally and each person in the sample is asked to try the new perfume and list his/her preference. The following table reports the results. Gender Men Women Men Women America Europe Asia 120 180 80 120 Preference 210 370 290 330 150 310 150 190 Like it Don't like it a. What is the probability that a randomly selected marn b. What is the probability that a randomly selected c. What is the probability that a randomly selected d. What is the probability that a randomly selected e. Are the events "Men" and "Like Perfume" likes the perfume? Asian likes the perfume? European woman does not like the perfume? American man does not like the perfume? independent in (i) America, (ii) Europe, (ii) Asia? Explain using probabilities. f. Internationally, are the events "Men" and "Like Perfume" independent? Explain using probabilities.

Explanation / Answer

a) probability =P( liker it|men) =480/(480+520)=0.48

b)probability =P( loke it|Asian) =(120+180)/500 =0.6

c)probability =P( do not like|European Women) =190/(190+310)=0.38

d) probability =P( do not like|American Men) =290/(210+290)=0.58

e)(i) in America : P(Men)*P( like perfume) =(210+290)/1200 *(210+370)/1200 =0.2014

and P( Men and Like perfuime) =210/1200=0.175

as they are not equal ; not independent.

(ii)

in Europe : P(Men)*P( like perfume) =(150+150)/800 *(150+310)/800 =0.2156

and P( Men and Like perfuime) =150/800=0.1875

as they are not equal ; not independent.

(iii)

in Asia : P(Men)*P( like perfume) =(120+80)/500 *(120+180)/500 =0.24

and P( Men and Like perfuime) =120/500=0.24

as they are equal ; therefore independent.

f)internationally:

P(Men)*P( like perfume) =(520+480)/2500 *(860+480)/2500 =0.2144

and P( Men and Like perfuime) =480/2500=0.192

as they are not equal ; therefore not independent.

America Europe Asia total like it Men 210 150 120 480 Women 370 310 180 860 do not like it Men 290 150 80 520 Women 330 190 120 640 total 1200 800 500 2500

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