AP®︎ Statistics (pre-2026): Unit 5 Flashcards

The natural sample-to-sample differences in a statistic when random samples come from the same population.

Random variation comes from chance in sampling; nonrandom variation comes from bias or other systematic causes.

A parameter describes the whole population; a statistic describes a sample and estimates the parameter.

x̄ and p̂ describe samples, while μ and p describe populations.

The distribution of a statistic from all possible samples of a fixed size from a population.

A variable that can take any value within an interval, with probabilities assigned to intervals.

The area over an interval equals the probability that a value falls in that interval.

All area equals 1, and a normal curve has 0.5 on each side of the mean.

About 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations.

The normal distribution with mean 0 and standard deviation 1, used with z-scores.

Standardize if needed, then use a table or technology to find area for the interval.

Use z-scores or technology to find boundary values, then convert back to the original scale.

A distribution can be modeled normally if it is roughly symmetric and bell-shaped.

Convert values from different distributions to standardized units so their relative positions can be compared.

A continuous, symmetric, unimodal bell-shaped distribution determined by its mean and standard deviation.

A standardized value showing how many standard deviations an observation is from the mean.

Areas under a normal curve can describe left-tail, right-tail, middle, or split-tail intervals.

The percent of observations in a distribution that are at or below a value.

For large independent random samples, the sampling distribution of the sample mean is approximately normal.

Independent observations and a sufficiently large random sample, often n at least 30.

Generate many repeated random samples from a population and calculate the statistic each time.

A distribution of simulated statistics created under assumed parameter values or random reassignment.

Use it for probabilities about sample means when the population shape is unknown but conditions are met.

Larger samples produce less spread in the sampling distribution, so statistics cluster more closely around the population parameter and estimates are more precise.

A sample statistic used to estimate a population parameter.

The single numerical value of a statistic from one sample.

A statistic whose sampling distribution is centered at the true parameter.

A statistic whose sampling distribution is not centered at the true parameter.

The amount sample estimates differ from one sample to another.

x-bar estimates mu and is unbiased because its mean equals mu.

p-hat estimates p and is unbiased because its mean equals p.

An estimator with little bias and low variability across repeated samples.

The natural difference between a sample statistic and the true population parameter.

The distribution of possible p-hat values from many repeated random samples of size n.

Mean equals p; standard deviation equals sqrt(p(1-p)/n) for independent samples.

When sampling without replacement, n should be less than 10% of the population size.

Without replacement, variability is slightly smaller than sqrt(p(1-p)/n).

If large counts are met, p-hat is approximately normal in repeated sampling.

Describe center, spread, or probability using proportions and the specific population context.

Approximate normality requires at least 10 expected successes and 10 expected failures.

The proportion of successes in a sample, written as p-hat.

The distribution of possible differences between two sample proportions from repeated independent samples.

Mean is p1 - p2; standard deviation is √[p1(1-p1)/n1 + p2(1-p2)/n2].

Two groups whose samples are selected so one sample's outcomes do not affect the other's.

With replacement uses the standard formula; without replacement gives a slightly smaller standard deviation.

If each sample is less than 10% of its population, ignoring replacement has negligible effect.

Describe center and spread as differences in population proportions using the problem's groups and units.

The distribution is approximately normal when all four expected counts are at least 10.

The distribution of all possible sample means from repeated random samples of size n.

Without replacement, spread is slightly smaller; if n is under 10% of N, the difference is negligible.

If the population distribution is normal, the sample mean distribution is normal for any sample size.

Describe x̄ by its shape, mean μ, and standard deviation σ/√n with appropriate conditions.

State chances about sample means in context, using the variable’s units and the population described.

For independent sampling, the center is μ and the spread is σ/√n.

The distribution of possible differences between two sample means from repeated random samples.

Mean is μ1 - μ2; standard deviation is √(σ1²/n1 + σ2²/n2) for independent samples.

Samples chosen so one sample's outcomes do not affect the other's outcomes.

With replacement uses the usual formula; without replacement gives a slightly smaller standard deviation.

If each sample is under 10% of its population, ignoring reduced spread without replacement is acceptable.

State center, spread, or probability in context, with correct units, for the two populations.

It is normal if populations are normal, or approximately normal when both samples are at least 30.