FE515 – Sampling and Estimation

Sampling

Sampling Error

In statistics, we calculate sample statistics in order to estimate our population parameters.

Sampling error of the mean = sample mean $\overline{x}$$\bar x$ - population mean $\mu$$\mu$.

Sample statistic itself is a random variable and has a probability distribution.

Central Limit Theory

With large $n$$n$ (sample size) the sampling distribution of the sample mean approaches $\mathcal{N}(\mu ,\frac{{\sigma }^2}{n})$$\mathcal N(\mu,\frac{\sigma^2}{n})$.

Estimation

Properties of Estimation

The desireable properties of an estimator :

• Unbiased - $E[\overline{x}]=\mu$$E[\bar x] = \mu$

• Efficiency - has vervy small Variance

• Consistency - if sample size $n$$n$ increases, standard deviation of the parameter decreases

Point & Confidence Interval Estimate

Degree of confidence = 1- $\alpha$$\alpha$

- $\alpha$$\alpha$ the level of confidence.