AP®︎ Statistics: Topic 4.7 Flashcards

Confidence interval procedure for estimating μ1 − μ2 from two independent groups with a quantitative response when population standard deviations are unknown

μ1 − μ2: the difference between the two population means, stated in context with the response variable, populations, and subtraction order

Data come from two independent random samples or from a randomized experiment with random assignment to two treatments; the two groups must be independent, not matched

When sampling without replacement, each sample size must be no more than 10% of its population: n1 ≤ 0.10N1 and n2 ≤ 0.10N2; not needed for randomized experiments

Sampling distribution of x̄1 − x̄2 is approximately normal: both populations are approximately normal, or both n1 and n2 are at least 30, or if either sample is under 30 then both samples show no strong skewness or outliers

x̄1 − x̄2, the difference between the sample means

SE = √(s1^2/n1 + s2^2/n2), the estimated variability of the difference in sample means

ME = t*√(s1^2/n1 + s2^2/n2)

(x̄1 − x̄2) ± t*√(s1^2/n1 + s2^2/n2)

Usually found with technology; df may be noninteger and falls between min(n1 - 1, n2 - 1) and n1 + n2 - 2. If using a t-table, use df = min(n1 - 1, n2 - 1) as a conservative choice

The standard AP Stats method for two means; it does not assume equal population variances, so calculator pooled setting should be No

Matched pairs uses pairwise differences and a one-sample t-interval; independent two-sample means uses two unrelated groups and a two-sample t-interval

The order in μ1 − μ2 must match x̄1 − x̄2, the reported interval, and the units context; reversing the order changes only the sign

TI-84 command for a two-sample t-interval for μ1 - μ2; enter x̄1, s1, n1, x̄2, s2, n2, choose the confidence level, and set pooled to No

Positive critical value from the appropriate t-distribution that leaves the central C% between -t* and t*.