Problem 2. In a study of the possible association between age and the preference

Question

Problem 2. In a study of the possible association between age and the preference for a new type of natural sweetener, the manufacturer conducted a survey. They wanted to see if those who preferred the new sweetener to sugar differed from those who liked sugar better, with respect to age. Of the 20 people who liked sugar, 11 were younger than 18 years old, compared to 13 out of 45 sweetener lovers. Based on this study, should the company begin an advertising campaign targeting the young consumers? Why or why not? 5 command opt command

Explanation / Answer

Here

sample proportion for people who liked sugar, p^1 = 11/20 = 0.55

Sample proportion for people who liked sweetner p^2 = 13/45 = 0.2889

Here pooled estimate = p = (11 + 13)/ (20 + 45) = 0.3692

standard error of proportion = SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] } = sqrt [0.3692 * 0.6308 * (1/20 + 1/45) ] = 0.1297

Test statistic

Z = (0.55 - 0.2889)/0.1297 = 2.013

so p - value = Pr(Z < 2.013) = 0.022

Here p - value < 0.05 so we can say that compay should market its product to young customers.

Here we are making it on the recommendations of Z test for two sample proportion.

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