Using the results in Table 4.2, estimate the probability that a randomly selecte

Question

Using the results in Table 4.2, estimate the probability that a randomly selected 21- to 49-year-old consumer would :

. (a) Give the phrase a rating of 4 or 5 given that the consumer is male; give the phrase a rating of 4 or 5 given that the consumer is female.

Based on these results, is the appeal of the phrase among males much different from the appeal of the phrase among females? (Round to 4 decimal places.)

P(4 or 5 | Male) = P(4 or 5 | Female) =???? , the difference is ????

Give the phrase a rating of 4 or 5, given that the consumer is in the 21–24 age group; given that the consumer is in the 25–34 age group; given that the consumer is in the 35–49 age group. Based on these results, which age group finds the phrase most appealing? Least appealing? (Round to 4 decimal places.)

P(4 or 5 | age 21 – 24) =?????

P(4 or 5 | age 25 – 34) = ?????

P(4 or 5 | age 35 – 49) = ????

Most appealing:????

Least appealing:?????

Gender Age Group Rating Total Male Female 21–24 25–34 35–49 Extremely appealing (5) 151 68 83 48 66 37 (4) 91 51 40 36 36 19 (3) 36 21 15 9 12 15 (2) 13 7 6 4 6 3 Not at all appealing (1) 9 3 6 4 3 2

Explanation / Answer

(a) The given condition forms the denominator of the probability and we get the count of favourable events.

First, The probability of a 4 or 5 stars given we are picking a random individual with known that the chosen person is male. So the denominator is the total number of male individuals = 150. and number of favourable events = number of male giving 4 or 5 stars = 119. So the required probability = P(4 or 5| Male) = 119/150 = 0.7933

Now to find P(4 or 5|Female) = total number of female giving 4 or 5/total number of female = 123/150 = 0.8200

So the appeal of phrase is slightly lower than to female. the difference is 0.8200 - 0.7933 = 0.0267

(b) Now we are to calculate the appealing of phrase probability by age group.

First, P(4 or 5| age is in group 21-24) = number of 4 or 5 rating in age group 21-24 / number of individuals in group 21-24 = 84/101 = 0.8317

Second, P(4 or 5| age is in group 25-34) = number of 4 or 5 rating in age group 25-34 / number of individuals in group 25-34 = 102/123 = 0.8293

Third, P(4 or 5| age is in group 35-49) = number of 4 or 5 rating in age group 35-49 / number of individuals in group 35-49 = 56/76 =  0.7368

So phrases are most appealing to age group of 21-24 and least appealing to age group 35-49, i.e. the appeal of phrases decrease with increasing age.

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