Foundations for Inference Practice Flashcards

A set of vocabulary flashcards covering the key definitions and formulas of sampling distributions for means and proportions, as well as the Central Limit Theorem.

Parameters

Numerical descriptive measures for populations, such as $\mu$ and $\sigma$ for normal distributions or $p$ for binomial distributions.

Statistics

Numerical descriptive measures calculated from a sample; because they vary from sample to sample, they are considered random variables.

Sampling Distributions

Probability distributions for statistics that indicate what values the statistics can take and how often each value occurs in repeated sampling.

Central Limit Theorem (CLT)

States that if random samples of $n$ observations are drawn from a nonnormal population with finite $\mu$ and $\sigma$, the sampling distribution of the sample mean $\bar{x}$ is approximately normal when $n$ is large.

Standard Error (SE) of the Sample Mean

The standard deviation of the sampling distribution of $\bar{x}$, calculated as $\frac{\sigma}{\sqrt{n}}$. It decreases as the sample size $n$ increases.

Sample Size Rule for Skewed Populations

When the sample population is skewed, the sample size must be at least $30$ before the sampling distribution of $\bar{x}$ becomes approximately normal.

Sample Size Rule for Normal Populations

If the original population is normal, the sampling distribution of $\bar{x}$ will be normal for any sample size.

Z-score for the Sample Mean

The formula used to standardize the sample mean: $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$.

Sample Proportion (\text{$\hat{p}$})

A statistic calculated as $\hat{p} = \frac{x}{n}$, used as the best guess for an unknown population proportion $p$.

Standard Error (SE) of the Sample Proportion

The standard deviation of the sampling distribution of $\hat{p}$, calculated as $\sqrt{\frac{pq}{n}}$. If $p$ is unknown, $\hat{p}$ is used as a substitute.

Success-Failure Condition

The requirement that $np \geq 10$ and $n(1 - p) \geq 10$ for the sampling distribution of the sample proportion to be considered sufficiently large for the Central Limit Theorem to hold.

Z-score for the Sample Proportion

The formula used to standardize a sample proportion: $z = \frac{\hat{p} - p}{\sqrt{\frac{pq}{n}}}$. Logic requires the distribution to be approximately normal, usually met when $np \geq 10$ and $nq \geq 10$.