ECON10005 Lecture Notes - Lecture 12: Random Variable, Confidence Interval, Sampling Distribution
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Known as a point estimate of the population mean. When computing a sample mean we"re observing a realisation of a random variable. Sample mean converges to population mean as n . We use the sample mean ((cid:3365)) to estimate an unknown population mean () Value of is a function of the sample. Is a realisation of a random variable (cid:3364) which is defined as, (cid:3364) is the estimator random variable that generates estimates: is the estimate. As n becomes infinitely large, the samplying distribution of (cid:3364) will converge to a normal that is centred around the true population mean. The central limit theorem allows us to approximate the sampling distribution when sample sizes are greater than 30. Sampling of the sample mean is given by the central limit theorem, which states. Distribution of an estimator is known as a sampling distribution. Point estimate could be very close/far away from the unknown population mean.