Starnes/Tabor, The Practice of Statistics for the AP® Course, 7e, Unit 6, English

point estimate

Specific value of a point estimator from a sample.

point estimator

Statistic that provides an estimate of a population parameter.

confidence interval

Gives a set of plausible values for a parameter based on sample data. Confidence intervals have the form, point estimate ± margin of error, or alternatively, statistic ± (critical value)(standard error of statistic).

confidence level C

Gives the approximate percentage of confidence intervals that will capture the population parameter in repeated random sampling with the same sample size.

margin of error

Describes how far, at most, we expect the point estimate to vary from the population parameter. That is, the difference between the point estimate and the population parameter will be less than the margin of error in C% of all samples, where C is the confidence level.

critical value

Multiplier that makes a confidence interval wide enough to have the stated capture rate. The critical value depends on both the confidence level C and the sampling distribution of the statistic.

standard error of ρ̂

The standard error describes how much the sample proportion ρ̂ typically varies from the population proportion p in repeated random samples of size n.

one-sample z interval for a proportion

Confidence interval used to estimate a population proportion p.

significance test

Formal procedure for using observed data to decide between two competing claims (the null hypothesis and the alternative hypothesis). The claims are usually statements about parameters. Also called a test of significance, a hypothesis test, or a test of hypotheses.

null hypothesis H₀

Claim we weigh evidence against in a significance test. Often the null hypothesis is a statement of "no difference."

alternative hypothesis Hₐ

The claim that we are trying to find evidence for in a significance test.

one-sided alternative hypothesis

An alternative hypothesis is one-sided if it states that a parameter is greater than the null value or if it states that the parameter is less than the null value. Tests with a one-sided alternative hypothesis are sometimes called one-sided tests or one-tailed tests.

two-sided alternative hypothesis

The alternative hypothesis is two-sided if it states that the parameter is different from the null value (it could be either greater than or less than). Tests with a two-sided alternative hypothesis are sometimes called two-sided tests or two-tailed tests.

P-value

The probability of getting evidence for the alternative hypothesis Hₐ as strong as or stronger than the observed evidence when the null hypothesis H₀ is true. The smaller the P-value, the stronger the evidence against H₀ and in favor of Hₐ provided by the data.

significance level α

Value that we use as a boundary to decide if an observed result is unlikely to happen by chance alone when the null hypothesis is true. The significance level gives the probability of a Type I error.

standardized test statistic

Value that measures how far a sample statistic is from what we would expect if the null hypothesis H₀ were true, in standard deviation units.

one-sample z test for a proportion

A significance test of the null hypothesis that a population proportion p is equal to a specified value.

Type I error

An error that occurs if we reject H₀ when H₀ is true. That is, the data give convincing evidence that Hₐ is true when it really isn’t.

Type II error

An error that occurs if we fail to reject H₀ when Hₐ is true. That is, the data do not give convincing evidence that Hₐ is true when it really is.

power

The probability that a test will find convincing evidence for Hₐ when a specific alternative value of the parameter is true. The power of a test against any alternative is 1 minus the probability of a Type II error for that alternative; that is, power = 1 - P(Type II error).

two-sample z interval for a difference in proportions

Confidence interval used to estimate a difference in the proportions of successes for two populations or treatments.

two-sample z test for the difference in proportions

A significance test of the null hypothesis that the difference in the proportions of successes for two populations or treatments is equal to a specified value (usually 0).