Sampling Distributions(KA/SAP/U10SamplingDistributions)

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Unit 10: Sampling Distributions

What is a sampling distribution?

A sampling distribution is the probability distribution of a given statistic based on a random sample. It shows how the value of a statistic (like the mean or proportion) varies from sample to sample, even when all samples are drawn from the same population. Sampling distributions are fundamental in inferential statistics because they allow us to estimate the variability of a statistic and make probability-based conclusions about a population.

Sampling distribution of a sample proportion

The sampling distribution of a sample proportion describes the distribution of sample proportions (\( \hat{p} \)) from all possible samples of the same size from a population. If the population proportion is \( p \) and the sample size is \( n \), the mean of the sampling distribution is \( p \) and the standard deviation is \( \sqrt{\frac{p(1-p)}{n}} \). For large enough samples, the distribution is approximately normal (by the Central Limit Theorem).

Sampling distribution of a sample mean

The sampling distribution of a sample mean describes the distribution of sample means (\( \bar{x} \)) from all possible samples of the same size from a population. If the population mean is \( \mu \) and the standard deviation is \( \sigma \), the mean of the sampling distribution is \( \mu \) and the standard deviation is \( \frac{\sigma}{\sqrt{n}} \). For large enough samples, the distribution is approximately normal (Central Limit Theorem).

Quiz: Test Your Understanding

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