A two-sample t interval estimates μ₁ − μ₂, the difference between two population means, from two independent samples. Enter the summary statistics, pick a confidence level, and follow each step from the point estimate to the interval. Then build 50 intervals at once to see what the confidence level really promises.
Enter the summary statistics for two independent groups and choose a confidence level. Every step of the interval is worked out below, the same way a 2-SampTInt does it.
Pretend the preset's sample statistics are the true population values. Draw new random samples of the same sizes, build an interval from each, and count how many capture the true difference μ₁ − μ₂.
The interval estimates the difference between two population means. Always define it in context: "μ₁ − μ₂ = the true difference in mean exam score (app users − non-users)."
We rarely know σ₁ and σ₂, so we plug in the sample standard deviations. The result, √(s₁²/n₁ + s₂²/n₂), is the standard error. Using s instead of σ is why we use t* instead of z*.
Technology uses a formula that gives a df between the smaller n − 1 and n₁ + n₂ − 2. If you must use a table, use the smaller of n₁ − 1 and n₂ − 1. That gives a larger t* and a slightly wider, "conservative" interval.
Random: two independent random samples or a randomized experiment. 10%: each sample is at most 10% of its population (when sampling). Normal/Large sample: each n ≥ 30, or the sample data show no strong skew or outliers.
"We are C% confident that the interval from a to b captures the true difference in mean [variable] for [group 1] minus [group 2]." Say which group was subtracted from which.
95% confidence means that if we repeated the sampling many times, about 95% of the intervals made this way would capture μ₁ − μ₂. It is not the probability that this one interval is right.
Critical values t* change with df. These are the values a table would give for a few df.
AP-style multiple choice. Pick an answer to see the explanation.
The vocabulary for topic 4.7. Read the list, flip through flashcards, or quiz yourself. For every term in the unit, see the Unit 4 terminology guide.