AP®︎ Statistics: Topic 3.3 Flashcards

An interval estimate for a population parameter; a range of plausible values for the parameter based on sample data

The proportion of the population in the success category; fixed but unknown

The statistic x/n; the point estimate of the population proportion p

The response category being counted in a categorical variable; just a label, not necessarily a favorable outcome

A statement that names the proportion, the success/response category, and the population of interest

The sample statistic used to estimate a population parameter; for a proportion interval, it is p̂.

The data must come from a random sample from the population of interest

When sampling without replacement, the population size must be at least 10 times the sample size: N ≥ 10n

The observed numbers of successes and failures must both be at least 10: x ≥ 10 and n − x ≥ 10, equivalently n p̂ ≥ 10 and n(1 − p̂) ≥ 10

The standard normal value with −z* and z* enclosing the middle C% of the distribution for the chosen confidence level

90%: 1.645; 95%: 1.960; 99%: 2.576

SE = √(p̂(1−p̂)/n); the estimated standard deviation of the sampling distribution of p̂, describing the typical sampling variability of p̂ around p

MOE = z*√(p̂(1−p̂)/n); the amount added to and subtracted from p̂, equal to half the interval width

Point estimate ± margin of error; for a proportion interval, center = p̂ and MOE is half the interval width

n = (z*^2 p̂(1−p̂)) / MOE^2; round up to the next whole number

Use p̂ = 0.5 in the sample-size formula when no reasonable estimate is available; it gives the largest required sample size

The confidence interval procedure for estimating one population proportion p: p̂ ± z*√(p̂(1−p̂)/n)