06 Sampling and Sampling Distributions Free Online FlashCards

What distinguishes a population from a sample?

A population is the complete set of individuals or measurements of interest; a sample is a subset selected from that population.

What defines a simple random sample?

In simple random sampling, every possible sample of the specified size has an equal chance of selection.

How does stratified sampling work?

Stratified sampling divides the population into meaningful, nonoverlapping strata and randomly samples from each one.

What is cluster sampling?

Cluster sampling randomly selects naturally occurring groups, then surveys every member or samples members within the chosen clusters.

How is a systematic sample selected?

Systematic sampling selects every $k$th member of an ordered list after choosing a random starting point; commonly, $k\approx\frac{N}{n}$.

Why can a large convenience sample still be misleading?

Convenience and voluntary-response samples can suffer selection bias because participants may differ systematically from nonparticipants. A larger sample does not automatically remove this bias.

What is a sampling distribution?

A sampling distribution is the probability distribution of a statistic over all possible random samples of a specified size.

What is the standard error of a sample mean?

For independent observations, the sample mean has standard error $\operatorname{SE}(\bar{X})=\frac{\sigma}{\sqrt{n}}$. In practice, estimate it with $\frac{s}{\sqrt{n}}$.

How much must sample size increase to halve standard error?

To cut the standard error in half, multiply the sample size by four, because standard error decreases with $\sqrt{n}$.

When is the finite population correction appropriate?

For sampling without replacement from a substantial fraction of a finite population, multiply $\frac{\sigma}{\sqrt{n}}$ by $\sqrt{\frac{N-n}{N-1}}$.

What does the Central Limit Theorem explain?

Under suitable conditions, the Central Limit Theorem says the sampling distribution of $\bar{X}$ becomes approximately Normal as $n$ increases, even if the population is not Normal.

When is a sample proportion approximately Normal?

When $np\ge 10$ and $n(1-p)\ge 10$, the sampling distribution of $\hat{P}$ is commonly treated as approximately Normal, with standard error $\sqrt{\frac{p(1-p)}{n}}$.