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    Working with sampling distribution and probability.

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    A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

    a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

    b) Find P(p^ >= 0.05)

    c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

    d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.

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    Solution Preview

    a) If the true unemployment rate is 6%, then let X be the number of people who were unemployed. Obviously,
    X~b(700,0.06), that is a binomial distribution with n=700, and p=0.06. So p^=(X1+X2+...+X700)/700 approximately follows normal distribution, where
    <br> E(p^)={E(X1)+E(X2)+...+E(X700)}/700=0.06,
    <br>and
    <br> ...

    Solution Summary

    A southern state has an unemployment rate of 6%. The state conducts monthly surveys in order to track the unemployment rate. In a recent month, a random sample of 700 people showed that 35 were unemployed.

    a) If the true unemployment rate is 6%, describe the sampling distribution of p^.

    b) Find P(p^ >= 0.05)

    c) Assume the population proposal, p, is unknown. Describe the sampling distribution of p^ based on the most recent sample.

    d) Find the probability that the sample proportion will lie within 0.05 of the true proportion of people who are unemployed.

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