AP®︎ Statistics: Topic 4.8 Flashcards

The parameter: population mean for group 1 minus population mean for group 2 for the same quantitative variable

Which group is first and which is second in μ₁ − μ₂; it determines the sign and meaning of the interval

Based on the samples or randomized experiment, there is C% confidence that the interval from a to b contains the true difference in the population means, in the stated order and context

In repeated random sampling of the same sizes from the same populations, about C% of intervals made by the same method will capture μ₁ − μ₂

If 0 is in the interval, there is insufficient evidence that the population means differ; if 0 is not in the interval, there is convincing evidence that the population means differ

For an interval estimating μ₁ − μ₂: all positive values support μ₁ > μ₂, all negative values support μ₁ < μ₂, and an interval containing 0 does not give sufficient evidence that the means differ

Including 0 means equal means are plausible, not that the population means are definitely equal

An interval outside 0 gives convincing evidence of a difference, but not certainty, because the method can miss the true parameter

μ₁ − μ₂ is the population difference being estimated; x̄₁ − x̄₂ is the sample difference and point estimate

If an interval for μ₁ − μ₂ is (a, b), the equivalent interval for μ₂ − μ₁ is (−b, −a)

Random samples support generalizing to the sampled populations; random assignment supports cause-and-effect about treatments

For the same model and standard-error method, a two-sided C% confidence interval excluding 0 matches rejecting H₀: μ₁ − μ₂ = 0 at α = 1 − C/100; including 0 matches failing to reject H₀

For an interval estimating μ₁ − μ₂, if d is inside the interval, d is plausible; if d is outside, the interval gives evidence against μ₁ − μ₂ = d

An interval can show convincing evidence of a difference without showing the difference is large enough to matter in context