Roper Checkbook

    by on Apr.15, 2009, under Leather Credit Card Holder

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    Roper Checkbook
    Roper Checkbook
    another stat question... ?


    Roper ASW conducted a survey to learn about American adults' attitudes twoard money and happiness. 56% of the respondents said they balance their checkbook at least once a month. Suppose a sample of 400 American adults were selected.

    What is the probability that the sample proportion will be within ±.02 if the population proportion?

    Let p be the population proportion of the respondents said they balance their checkbook at least once a month.

    Since n*p= 400*56%=224 and n*(1-^p)=400*(1-56%)=176 are both at least greater than 5, then n is considered to be large and so the sampling distribution of sample proportion-^p will follow the z standard normal distribution. This sampling distribution will have the mean of the sample proportions = U^p = p = 56% = 0.56 and the standard deviation of the sample proportions = δ^p = √[p(1-p)/n] =
    √[0.56*(1-0.56)/400] = √0.000616

    The lower limit of the sample proportion which is less than or equal to 0.02 from the population proportion
    = 0.56-0.02
    = 0.54

    The upper limit of the sample proportion which is less than or equal to 0.02 from the population proportion
    = 0.56+0.02
    = 0.58

    So,
    P(0.54<^p<0.58)
    = P{[(0.54-0.56)/√0.000616]<[(^p-p)/δ^p]<
    {[(0.58-0.56)/√0.000616]}
    = P(-0.81 = P(-0.81 = 0.2910 + 0.2910
    = 0.582

    So, there is a 0.582 probability that the sample proportion will be within ±.02 of the population proportion.

    Hope this helps.



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