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Math Help - Finding confidence intervals

  1. #1
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    Finding confidence intervals

    I am working on a large problem that is broken down into steps. The goal is to find the 95% confidence interval for p(x=1).

    X takes on the value 1 if unemployed, 0 otherwise.
    Y takes on the value 1 if no response, 0 otherwise.

    I have theta = pr(X=1), theta1= pr(X=1, Y=0) and theta2 = pr(Y=1).

    I need to find estimators for theta 1 and theta 2 and prove they are unbiased given the following information.
    We sent out n questionnaires. We received n1 back, and of that n1, m are unemployed.

    My estimators are:
    theta1hat = m/n1
    theta2hat = (n-n1)/n

    I am confused on how to show they are unbiased. I know to take the expectation, but don't know how to actually do that.

    Thanks in advance.
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  2. #2
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    Re: Finding confidence intervals

    Just realized something, is this because it is the expected value of a constant?

    My next step is to find the variance of theta1hat, which I assume is 0 because E(m^2/n1^2) - E(m/n1)2 = 0.

    Are these assumptions correct?
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