Question

) In the mid-1990s, Colgate-Palmolive developed a new toothpaste for the U.S. market, Colgate Total, with an antibacterial ingredient that was already being successfully sold overseas. At that time, the word antibacterial was not allowed for such products by the Food and Drug Administration (FDA). In response, the name “Total” was given to the product in the United States. The one word would convey that the toothpaste is the “total” package of various benefits. Young & Rubicam developed several commercials illustrating Total’s benefits and tested the commercials with focus groups. One commercial touting Total’s long-lasting benefits was particularly successful. The product was launched in the United States in January of 1998 using commercials that were designed from the more successful ideas of the focus group tests. Suppose 32% of all people in the United States saw the Total commercials. Of those who saw the commercials, 40% purchased Total at least once in the first 10 months of its introduction. According to U.S. Census Bureau data, approximately 20% of all Americans were in the 45-64 age category. Suppose 24% of the consumers who purchased Total for the first time during the initial 10-month period were in the 45-64 age category. Within three months of the Total launch, Colgate-Palmolive grabbed the number one market share for toothpaste. Ten months later, 21% of all U.S. households had purchased Total for the first time. The commercials and the new product were considered a success. During the first 10 months of its introduction, 43% of those who initially tried Total purchased it again. a) What percentage of U.S. households purchased Total at least twice in the first 10 months of its release? b) Can you conclude the initial purchase of Total was independent of age? Use a quantitative argument to justify your answer. c) Calculate the probability that a randomly selected U.S. consumer is either in the 45-64 age category or purchased Total during the initial 10-month period. d) What is the probability that a randomly selected person purchased Total in the first 10 months given that the person is in the 45-64 age category? e) What percentage of people who did not see the commercials purchased Total at least once in the first 10 months of its introduction?

Answer 1

Answer for (a)

As per the given data & information

So the write up states that 21% of all households purchased total for the first time and 43% of this purchased it againin the same time period so the percentage of US households who pourchased it twice is 0.43*0.21= 0.09

Thus 9% of all the US households purchased it twice

Answer for (b)

As per the given data & information

Now 20% of all americans are in the 45-64 age group and 24% of the consumers who purchased for the first time were in the 45-64 age group so 0.24*0.21*X = 0.05X were 45-64 age who purchased and 0.20*X is the toal population of al 45-64 age groups, if X is the whole poplulation

This means that 5 out of 20 people in the 45-64 age group purchased total for the first time, hence age group is not independent of initial purchase

Answer for (c)

As per the given data & information

So 21 people in 100 purchased Total for the first time according to the write up if 100 is the total population and as per Q2 5 people out of these were in the 45-64 age group

So probability that a randomly selected person purchased total in the first 10 months given that he is in the 45-64 age group = 5/21 = 0.238

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