AP Stats Topic 14

Tests of Significance

assess the evidence for a claim about a population

Statistical Inference

Provides methods for drawing conclusions about a population from sample data

Upper Critical Value

the number z_a/2 with probability p lying to its right under the standard normal curve

Null Hypothesis

Says there is no effect or change in the population (H₀)

Test for significance

intended to access the evidence provided by data against a null hypothesis

Alternate Hypothesis

says there is an effect or change in the population (H_a)

One sided alternative

a parameter differs from its null value in a specific direction (</>)

Two sided alternative

a parameter differs from its null value in either direction (not =)

p value

the probability that the test statistic will take a value as extreme or more extreme than the value actually observed.

Statistically significant

the p value is as small or smaller than a specified value

Test statistic

based on a statistic that estimates the parameter that appears in the hypothesis (z, t, p, x², or f)

Decision Analysis

regards statistical inference in general as giving rules for making decisions in the presence of uncertainty

Power

measures a significance test’s ability to detect an alternative hypothesis

Type I Error

occurs when we reject H₀ when it is actually true

Type II Error

occurs when we accept H₀ when H_a is actually true

Acceptance Sampling

one such circumstance that calls for a decision or action as the end result of inference