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13 multiple-choice questions and 24 flashcards on Sampling Distributions and Inference for Means and Proportions, about 9% of the HS Statistics bank. Every one carries a written rationale.
Sampling Distributions and Inference for Means and Proportions is one of 7 chapters in CoStudy's HS Statistics bank, and it holds 13 of the bank's 150 multiple-choice questions — roughly 9% of the total. That proportion is not arbitrary: chapters follow the certifying body's published exam outline, and the number of questions in each is set by that domain's published weight, so the share of your practice time this chapter takes matches the share of the real exam it accounts for.
Studying by chapter is worth doing once you have a diagnostic score. A single overall percentage tells you whether you are close; it does not tell you which domain is dragging. Working a weak chapter in isolation, and re-testing it in isolation, is the fastest way to move a score that has stalled — and it is why the mock exams in CoStudy report by domain rather than as one number.
7 questions drawn from this chapter, with the full rationale shown — the controlling principle behind the right answer, and why each wrong option tempts and fails.
IQ scores are N(100, 15²). What proportion of people score between 85 and 115?
Answer: D — About 68%
D) 85 and 115 are exactly 1 SD below and above the mean (z = ±1). By the empirical (68-95-99.7) rule, ≈68% of normal data lies within 1 SD. A) Only the median split. B) Within 2 SDs. C) Within 3 SDs.
Two events A and B are INDEPENDENT iff:
Answer: E — P(A ∩ B) = P(A)·P(B) (independence definition)
Independence: P(A ∩ E) = P(A)·P(E). Equivalently P(A|E) = P(A). Distinct from mutually exclusive (A ∩ B empty). Independence is about no influence; mutually exclusive can't both occur.
In a normal distribution, approximately 68% of data falls within how many standard deviations of the mean?
Answer: C — 1
C) The empirical rule: ≈68% within 1 SD, ≈95% within 2 SD, ≈99.7% within 3 SD. B) That covers ~95%. A) That covers ~99.7%. D) Too narrow.
Normal distribution: ~68% of data lies within how many standard deviations of mean?
Answer: A — 1 (68-95-99.7 rule: about 68% within ±1σ, 95% within ±2σ, 99.7% within ±3σ)
Empirical rule (68-95-99.7): for normal distribution, about 68% of data within 1 SD, 95% within 2 SD, 99.7% within 3 SD. Foundation for outlier detection and confidence intervals.
Probability of rolling a 4 on a fair 6-sided die:
Answer: B — 1/6 (one favorable outcome out of 6 equally likely)
Classical probability: favorable outcomes / total equally likely outcomes. Die has 6 faces, only one is '4'. P = 1/6. Theoretical vs. empirical: from experiments, frequency approaches 1/6 by law of large numbers.
A two-tailed test produces a p-value of 0.08. At α = 0.05, the conclusion is:
Answer: D — Fail to reject H₀ — insufficient evidence to reject
D) p = 0.08 > α = 0.05, so we fail to reject H₀. We never "accept" H₀; we simply lack evidence to reject. A) Wrong direction. B) Hypothesis tests don't prove the null. C) Vague — the formal decision is clear at the chosen α.
Sample means x̄ are drawn from a population with μ = 50 and σ = 12, using n = 36. The sampling distribution of x̄ has:
Answer: C — Mean 50, SD 2
C) Sampling distribution of x̄ has mean μ = 50 and SD σ/√n = 12/√36 = 12/6 = 2. A) Forgot to divide by √n. B) Used √n = 2 instead of 6. D) Swapped mean and SD.
3 cards from the 24 in this chapter.
Common stats software?
Calculator, Excel, R, Python, SPSS, JMP. TI-83/84 standard for HS.
Sample space?
Set of all possible outcomes of a random experiment. P(sample space) = 1.
Stats in sports?
Performance analysis, sabermetrics, predictive models.
These are a sample. The full Sampling Distributions and Inference for Means and Proportions chapter runs 37 items with per-chapter progress tracking, on the web and in the iOS app.
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