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Can anyone help me solve this statistics problem?

1.A marketing research consultant hired by Coca-Cola is interested in determining if the proportion of customers who prefer Coke to other brands is more than 50%. A random sample of 200 consumers was selected from the market under investigation, 55% favored Coca-Cola over other brands. Using a 5% significance level, can the marketing consultant conclude that the proportion of customers who prefer Coca-Cola exceeds 50%?

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2 Responses to “Can anyone help me solve this statistics problem?”

  1. Harley F November 28, 2013 at 3:49 pm #

    I would say the answer is:

    No, they can’t because there needs to be more people asked if they like it before they make the decision to make it public that Coke-Cola has more people that like it than the other brands have.

    Hope I helped!!! :-)

  2. gab23 November 28, 2013 at 4:45 pm #

    Given that ^p = the sample proportion of customers who prefer Coca-Cola= 55% = 0.55, n= the number of customers selected in this particular random sample=200, p0= the claimed true value of the population proportion to be tested=50%=0.5 and α= level of significance= the chance of wrongly reject H0 when it is in fact true=5%=0.05.

    We wish to test
    Ho: p=p0
    p=50%
    i.e.,p=0.5
    versus
    Ha: p>p0
    p>50%
    i.e.,p>0.5

    Since n*P0= 200*0.5 = 100 and n*(1-P0)=200*(1-0.5)= 100 are both at least greater than 5, then n is considered to be large and so the sampling distribution of ^p is approximately normally distributed and so it is appropriate to describe and estimate the above probability distribution using the z score in this case.

    At α=5%=0.05 level of significance,
    the rejection point
    = zα
    = z0.05
    = 1.645

    The test static
    = z
    = (^p-p0)/√[p0*(1-p0)/n]
    = (0.55-0.5)/√[0.5*(1-0.5)/200]
    = 1.41

    In this case, we can only reject Ho in favor of Ha if and only if z>zα; or alternatively, if the p-value- the area under the standard normal curve to the right of z is less than our chosen value of α.

    Because z=1.41 is smaller instead of greater than our rejection point zα=z0.05=1.645, then we fail to reject Ho in favor of Ha at the α=0.05 level of significance. Then the market consultant cannot conclude that the proportion of customers who prefer Coca-Cola exceeds 50%. In addition, since the p-value of 0.0793-the area under the standard normal curve to the right of z=1.41 is much greater than instead of less than 0.01, then we don’t have any evidence at all to support that Ha is true in against Ho.

    Hope this helps.

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