Statistical Sciences 2141A/B Lecture Notes - Lecture 23: Central Limit Theorem, Bias Of An Estimator, Binomial Distribution
6 Nov 2018
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Recall that for large values of n, the normal approximation of the binomial distribution can be used. If x ~ b(n, p), then the sample proportion (unbiased estimator of p) has the approximate distribution. The standard error provides an indication of accuracy of a point estimate. Smaller values of the standard error indicate that the point estimate is likely more accurate because its variability about the true value is smaller. In the case of the success probability p, the standard error is unknown since it depends on p, but it can be estimated using the point estimate. Consider the unknown parameter p, which represents the probability that a machine breakdown is due to operator misuse. Suppose that a representative sample of n = 46 machine breakdowns is recorded, of which x = 13 are due to operator misuse. Find an standard error of the estimate of p.
