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5When mean > median, high-value outliers pull the mean rightward. Left-skew would give mean < median. Skew alone cannot confirm bimodality.

5Lower fence = 40 − 1.5(12) = 40 − 18 = 22. Upper fence = 52 + 1.5(12) = 52 + 18 = 70. Any point outside [22, 70] is an outlier.

5Plug x = 0: ŷ = 45 + 5.2(0) = 45. The y-intercept (45) is the predicted value when x = 0. D sounds intuitive but is not what the model says.

5r² ≠ r (A). r² describes explained variation, not slope (C). Correlation never implies causation and is never a "probability" of causation (D).

5Random assignment to treatments defines an experiment (C). Sampling methods (A, B) describe how subjects are selected from a population, not how they are assigned. Observational studies never impose a treatment (D).

5Cluster (A): randomly select entire groups. SRS (C): every individual equally likely, no grouping. Convenience (D): whoever is easiest — biased. Stratified (B): sample from each stratum.

5Independence → multiply: 0.4 × 0.5 = 0.20. A (0.9) uses addition = P(A∪B). 0.1 = 0.5 − 0.4 (subtraction, no rule). 0.45 = average of probabilities — meaningless here.

50.6 + 0.4 − 0.2 = 0.80. A (1.0) forgets to subtract overlap. C (0.24) multiplies instead. D (0.76) subtracts 0.24 from 1 — circular error.

5The CLT's power is that no matter what shape the population has, large enough n produces a normal sampling distribution. A is the very thing CLT frees us from needing.

5SE = 20 / √100 = 20/10 = 2. A forgets to divide. B divides by 100 instead of √100. D multiplies instead of divides.

5For proportions, normality is checked via the large counts condition (C), not n ≥ 30 (A, which applies to means). B applies to t-procedures, not proportions. D is never achievable with a sample.

5A is the classic error — the true proportion is fixed, not random; the interval either captures it or doesn't. "95% confidence" describes the long-run performance of the method, not this one interval. B and D misinterpret what varies.

5The t-distribution exists specifically because σ is unknown (C) and we substitute the sample s. With very large n the t and z converge, but we still formally use t. Proportions use z-procedures (D).

50.03 < 0.05 → reject H₀ (B). We never "accept" or "prove" H₀ (C) — we only fail to reject it. D is backwards. A would apply only if p ≥ α.

5A describes χ² test for independence/association (two-way table). B is a t-test for means. D is a one-proportion z-test. Goodness of fit (C) compares one variable's observed counts to expected counts from a stated model.

5The chi-square large counts condition requires all expected (not observed) counts ≥ 5. "At least 10" (A) is the large counts condition for proportions (np̂ ≥ 10). 30 (D) is for CLT of means.

5β = 0 means the line is flat — x has no predictive power over y. Although β = 0 ↔ r = 0, we state the null in terms of β (not r) for the slope test. D is actually the alternative hypothesis.

5Residual = y − ŷ (B). A reverses the sign. C is deviation from the mean (used in other formulas). D is a ratio — not a residual. A positive residual means the point lies above the line.

5The drug works (H₀ false), yet we fail to reject H₀ — that's a Type II error (B). Type I (A) would be rejecting H₀ when it's actually true. Low power makes Type II errors more likely, but the error itself is Type II, not "a power failure" (D).

5Larger n reduces SE, making it easier to detect a real effect → higher power (C). Smaller n (A) reduces power. Stricter α (B) makes it harder to reject → reduces power. Higher σ (D) adds noise → reduces power.