AP Statistics Vocab

simple random sample

Sampling design where every individual has an equal chance of being chosen.

Random Table of Digits

Every entry in the table has an equal probability of being any digit from 0-9. This is can be used to conduct a SRS

Stratified Random sample

Sampling design where the population is divided into homogenous groups called strata. An SRS is pulled from each strata. This can help control for lurking variables.

Systematic Random sample

Sampling design that uses a method of identifying subjects randomly before starting. For instance, every 10th customer is surveyed.

Cluster sample

Sampling design based on a location where a location is randomly picked and samples. For example, choosing a random zip code and then surveying all the houses. Each cluster is meant to represent and is similar to the population.

Multistage sample

Sampling design where there are at least 2 separate levels/stages of SRS. For example, in a student population, they are divided into seniors vs. juniors, then Honors vs. CP students, and then they are randomly selected. This uses a combination of different types of sampling methods, typically when the population is very large.

Observational study

observes individuals and measures variables without influencing

Experiment

Imposes a treatment on individuals to measure responses. This is the only way to understand cause and effect.

Law of Large Numbers

As sample size increases, the sample mean will approach the population mean.

Central Limit Theorem

Regardless of population shape, if n is greater or equal to 30, then the distribution of sample means will be approximately normal, with the mean of mu and standard deviation sigma/sqrt(n)

Mean, variance, and standard deviation for x → x+y

Mean: Mu(x)+Mu(y)

Variance: Sigmax² + Sigmay²

Standard deviation: Sqrt(Sigmax²+Sigmay²)

Mean, variance, and standard deviation for x → a+bx

Mean: a + b * Mu(x)

Variance: b² * Sigmax²

Standard Deviation: b * Sigmax

Mean, variance, and standard deviation for x → x-y

Mean: Mu(x)-Mu(y)

Variance: Sigmax² + Sigmay²

Standard deviation: Sqrt(Sigmax²+Sigmay²)

Type I Error

When you reject H0, but is it actually true. This is represented by alpha

Type II Error

When you fail to reject H0, but it is actually false. This is represented by beta

Power

Probability of rejecting null when it is really false (a correct decision)

Power = 1 - Beta (Type II error)

Matched-pairs t-test for a mean difference

Method used to test whether the mean difference between pairs of measurements is zero or not. It is used when your data values are paired measurements. For example, you might have before-and-after measurements for a group of people

point estimate

single value that serves as an approximation of a population parameter