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Need help with statistics

  1. Mar 2, 2005 #1
    Hi, I need help with this stats case study:


    In the mid-1990s, Colgate-Palmolive developed a new toothpaste for the U.S. , Colgate Total, with an anitbacterial ingredient that was already being successfully sold overseas. However, the word antibacterial was not allowed for such products by the Food and Drug Administration rules. So Colgate-Palmolive had to come up with another way of marketing this and other features of their new toothpaste to U.S. consumers. Market researchers told Colgate-Palmotive that consumers were weary of
    trying to discern among the different advantages of various toothpaste brands and wanted simplification in their shopping lives. 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 and 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. Meanwhile, in 1997, Colgate-Palmotive recieved FDA approval for Total, five years after the company had applied for it. The product was lunched in the United States in January of 1998 using commercials that were designed from the more successful ideas of the focus group tests. A print campaign followed.

    Within three months, Colgate grabbed the number one market share for toothpaste. Ten months later, 21% of all U.S. households had purchased Total (a product of Colgate) for the first time. During this same period, 43% of those who initially tried Total purchased it again. Colgate Total had been succesfully introduced into the U.S. market.


    1) Is age category independent of willingness to try new products? According to the U.S. Census Bureau, approximately 20% of all Americans are in the 45-64 age category. Supposese 24% of the consumers who purchased Total for the first time during the initial 10-month period were in the 45-64 age category. Use this information to determine whether age is independent of the initial purchase of Total during the introductory time period. Explain your answer.

    2) Using the probabilities given in Question 1, 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. 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?

    :confused:
     
  2. jcsd
  3. Mar 2, 2005 #2
    please show your work and ideas
     
  4. Mar 3, 2005 #3
    i ithink the first question deals with .43 x .21.
     
  5. Mar 5, 2005 #4
    anyone know how to solve this?
     
  6. Mar 5, 2005 #5

    xanthym

    User Avatar
    Science Advisor

    These problems utilize Conditional Probabilities having the following standard definition (the "|" symbol denotes "GIVEN"):
    Prob{Event_A | Event_B} = Prob{Event_A AND Event_B}/Prob{Event_B}


    Problem statements provide following data:
    Prob{Purchase_FirstTime} = 0.21
    Prob{Age_45-64} = 0.20
    Prob{Age_45-64 | Purchase_FirstTime} = 0.24

    Problem #1:
    By definition, Events "Age_45-64" and "Purchase_FirstTime" are independent if and only if:
    Prob{Age_45-64 AND Purchase_FirstTime} =?= Prob{Age_45-64}*Prob{Purchase_FirstTime} =
    = (0.20)*(0.21) = (0.042)
    We calculate Left side of the above equation from:
    Prob{Age_45-64 AND Purchase_FirstTime} =
    = Prob{Age_45-64 | Purchase_FirstTime}*Prob{Purchase_FirstTime} =
    = (0.24)*(0.21) = (0.0504)
    Since the 2 Blue values above are not equal:
    Events "Age_45-64" and "Purchase_FirstTime" are NOT independent.

    Problem #2:
    a)
    Prob{Age_45-64 OR Purchase_FirstTime} =
    = Prob{Age_45-64} + Prob{Purchase_FirstTime} - Prob{Age_45-64 AND Purchase_FirstTime} =
    = (0.20) + (0.21) - (0.0504)
    Prob{Age_45-64 OR Purchase_FirstTime} = (0.36)

    b)
    Prob{Purchase_FirstTime | Age_45-64} =
    = Prob{Age_45-64 AND Purchase_FirstTime}/Prob{Purchase_FirstTime} =
    = (0.0504)/(0.21)
    Prob{Purchase_FirstTime | Age_45-64} = (0.24)


    ~~
     
    Last edited: Mar 6, 2005
  7. Mar 6, 2005 #6
    oh i see thanks , so will using conditional properties work for the following problems as well? i'm lost in these two problems.

    3. 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. 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?

    4. Suppose 32% of all toothpaste consumers in the U.S. saw the Total commericals. Of those who saw the commercials, 40% purchased Total at least once in the first 10 months of its introduction. Of those who did not see the commercials, 12.06% purchased Total at least once in the first 10 months of its introduction. Suppose a toothpaste consumer is randomly selected and it is learned that they purchased Total during the first 10 months of its introduction. Revise the probability that this person saw Total commercials and the probability that the person did not see the Total commercials?
     
  8. Mar 10, 2005 #7
    still stuck, anyone knows?
     
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