The distribution of sample statistics (e.g., sample means) calculated from multiple samples taken from the same population.

The standard deviation of a sampling distribution; it measures the variability of sample statistics around the population parameter.

The CLT states that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases, regardless of the population distribution's shape.

The average value of a variable in the entire population.

The average value of a variable calculated from a sample of the population.

$\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}$

$\sigma_{\hat{p}} = \sqrt{\frac{p(1-p)}{n}}$

$\mu_{\bar{x}} = \mu$

The CLT states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. This allows us to use normal distribution properties for inference.

Sampling distributions allow us to make inferences about population parameters based on sample statistics. They provide a foundation for hypothesis testing and confidence intervals.

As the sample size increases, the standard error of the mean decreases. Larger samples provide more precise estimates of the population mean, reducing variability in the sampling distribution.

Standard error quantifies the variability of sample statistics (like the sample mean) around the true population parameter. It indicates how much sample means are likely to vary from the population mean.

The mean of the sampling distribution of the sample mean is equal to the population mean. This implies that the sample means are centered around the population mean.