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9 multiple-choice questions and 8 flashcards on Inference for Categorical Data: Chi-Square, about 6% of the HS Statistics bank. Every one carries a written rationale.
Inference for Categorical Data: Chi-Square is one of 7 chapters in CoStudy's HS Statistics bank, and it holds 9 of the bank's 150 multiple-choice questions — roughly 6% 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.
Confidence interval for mean with known σ: x̄ ± z*·(σ/√n). For 95% CI, z* ≈ ?
Answer: C — 1.96 (standard value from normal table for 95% CI)
95% CI critical z ≈ 1.96 (often approximated as 2). For 90% z ≈ 1.645; 99% z ≈ 2.576. CI uses ± z*·(σ/√n). Interpretation: 95% of such intervals would contain true μ.
Z-score: z = (x - μ)/σ measures:
Answer: D — Number of standard deviations x is from the mean (standardization)
Z-score standardizes any value to standard normal scale. z = (x-μ)/σ tells how many SD above (positive) or below (negative) the mean. Use z-tables to find probabilities. Enables comparison across distributions.
A test has μ = 80, σ = 10. Your score 95 has z-score:
Answer: B — 1.5 (z = (95-80)/10 = 15/10 = 1.5)
z = (x-μ)/σ = (95-80)/10 = 1.5. You scored 1.5 SD above mean. Look up in z-table: probability ≈ 93%-ile. Standardization enables interpretation regardless of original scale.
p-value less than significance level α (typically 0.05) leads to:
Answer: A — Reject null hypothesis
p < α → reject H₀ (statistically significant). p ≥ α → fail to reject H₀ (insufficient evidence). p-value: probability of observed (or more extreme) result if null were true. Common α = 0.05.
Type I error in hypothesis testing is:
Answer: A — Rejecting null when null is actually TRUE (false positive)
Type I error (α): reject H₀ when true (false positive). Type II error (β): fail to reject H₀ when false (false negative). Power = 1 - β = probability of correctly rejecting false null. Trade-off between α and β.
Central Limit Theorem (CLT) states:
Answer: C — Distribution of sample means approaches normal as n grows (typically n ≥ 30), regardless of population shape, with mean μ and SE σ/√n
CLT: sampling distribution of x̄ approaches normal as n grows. Even non-normal populations produce nearly-normal sample means. Foundation of frequentist inference, confidence intervals, hypothesis tests.
The Central Limit Theorem states that:
Answer: B — The distribution of sample means tends toward normal as sample size grows (given finite variance)
B) The CLT applies to the sampling distribution of the mean, not the underlying population. It needs finite variance and reasonable sample size. A/C/D) Misstate or invent properties.
1 cards from the 8 in this chapter.
Binomial distribution?
Discrete distribution. n trials, p success per trial. X = number successes. Has formula for P(X=k).
These are a sample. The full Inference for Categorical Data: Chi-Square chapter runs 17 items with per-chapter progress tracking, on the web and in the iOS app.
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