consistincy of the estimator for the standard error in the wald intervall

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recall that the wald intervall is as $\bar{X}_n - \frac{\sigma}{\sqrt{n}} z_\alpha <p<\bar{X}_n + \frac{\sigma}{\sqrt{n}} z_\alpha$ to make a confidence intervall out of it , we estimate $\sigma$ with is equal to $\sqrt{(1-p)p}$ with $\sqrt{(1-\bar{X}_n)\bar{X_n}}$
I am looking to,prove the consistency of that estimation, any idea?