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Question 1. Which component of the scientific method is primarily responsible for generating a testable statement about a population? A) Data collection B) Deductive reasoning C) Descriptive statistics D) Exploratory analysis Answer: B Explanation: Deductive reasoning derives specific hypotheses from general theories, creating testable statements. Question 2. The null hypothesis (H₀) is best described as: A) The hypothesis the researcher hopes to prove B) A statement of no effect or no difference C) Always a directional claim D) The same as the alternative hypothesis Answer: B Explanation: H₀ asserts that there is no relationship/effect, serving as the default position. Question 3. A researcher predicts that a new drug will increase blood pressure. Which hypothesis format is appropriate? A) H₀: μ = 0, H₁: μ > 0 B) H₀: μ = 0, H₁: μ ≠ 0 C) H₀: μ ≠ 0, H₁: μ = 0 D) H₀: μ > 0, H₁: μ = 0 Answer: A Explanation: A one‑tailed (directional) alternative (μ > 0) reflects the expectation of an increase.
Question 4. In hypothesis testing, the phrase “fail to reject H₀” means: A) H₀ is proven true B) There is insufficient evidence against H₀ C) The alternative hypothesis is false D) The test was performed incorrectly Answer: B Explanation: “Fail to reject” indicates the data did not provide enough evidence to discard the null. Question 5. Setting α = 0.01 reduces the probability of which error? A) Type I error B) Type II error C) Both Type I and Type II errors D) Neither error type Answer: A Explanation: α is the significance level; lowering it directly reduces the chance of a false positive (Type I). Question 6. Which factor most directly increases statistical power (1‑β)? A) Decreasing sample size B) Increasing α C) Using a less sensitive test D) Decreasing effect size Answer: B Explanation: A larger α makes it easier to reject H₀, thereby increasing power.
Explanation: It provides a formal hypothesis test for normality. Question 10. Levene’s test assesses: A) Normality of a single variable B) Homogeneity of variances across groups C) Correlation between two continuous variables D) Proportion differences in a contingency table Answer: B Explanation: Levene’s test evaluates whether group variances are equal, a key ANOVA assumption. Question 11. When should a researcher prefer a non‑parametric test over a parametric test? A) When the sample size is > 1000 B) When the data are ordinal or violate normality C) When the population variance is known D) When the hypothesis is directional Answer: B Explanation: Non‑parametric tests do not rely on distributional assumptions and work with ordinal or non‑normal data. Question 12. The standard error of the mean differs from the standard deviation because it: A) Measures spread of the entire population B) Decreases as sample size increases C) Is always larger than the standard deviation D) Is unrelated to sample size Answer: B
Explanation: SE = SD/√n, so it shrinks with larger n, reflecting greater precision of the mean estimate. Question 13. For a large sample (n > 30) with known population variance, the appropriate test for a single mean is: A) One‑sample t‑test B) One‑sample z‑test C) Paired t‑test D) One‑sample χ² test Answer: B Explanation: When σ is known and n is large, the z‑test is appropriate. Question 14. In a one‑sample t‑test, the test statistic is calculated as: A) (x̄ − μ₀)/(σ/√n) B) (x̄ − μ₀)/(s/√n) C) (x̄ − μ₀)·√n D) (x̄ − μ₀)·σ Answer: B Explanation: The t‑statistic uses the sample standard deviation (s) when σ is unknown. Question 15. Which situation calls for an independent‑samples t‑test? A) Comparing pre‑ and post‑test scores of the same students B) Comparing exam scores of two different classrooms C) Testing a single proportion against a known value D) Assessing correlation between height and weight
Answer: A Explanation: F = MS_between / MS_within, comparing variance explained by groups to residual variance. Question 19. If a one‑way ANOVA yields a significant F, the next step to locate specific group differences is: A) Re‑run the ANOVA with a different α B) Conduct post‑hoc pairwise comparisons (e.g., Tukey HSD) C) Compute a single t‑test for all groups together D] Ignore the result; ANOVA alone identifies differences Answer: B Explanation: Post‑hoc tests control for multiple comparisons while pinpointing which means differ. Question 20. Tukey’s HSD test controls the family‑wise error rate by: A) Adjusting α for each comparison individually B) Using the studentized range distribution C) Applying a Bonferroni correction automatically D) Ignoring variance heterogeneity Answer: B Explanation: Tukey’s HSD uses the studentized range to keep the overall Type I error at the desired level. Question 21. Which chi‑square test evaluates whether two categorical variables are independent? A) Goodness‑of‑fit test B) Test of homogeneity C) Test of independence
D) McNemar’s test Answer: C Explanation: The chi‑square test of independence assesses association in a contingency table. Question 22. In a chi‑square goodness‑of‑fit test, the degrees of freedom are calculated as: A) (rows − 1) × (columns − 1) B) Number of categories − 1 C) Number of observations − 1 D) (rows + columns) − 2 Answer: B Explanation: df = k − 1 where k is the number of mutually exclusive categories. Question 23. Pearson’s r measures: A) Linear correlation between two continuous variables B) Rank‑order correlation for ordinal data C) Association between two nominal variables D) Difference between two proportions Answer: A Explanation: Pearson’s r quantifies the strength and direction of a linear relationship. Question 24. Which correlation coefficient is appropriate for ordinal data? A) Pearson’s r B) Spearman’s rho C) Kendall’s tau D) Both B and C are acceptable
Answer: B Explanation: The p‑value is the conditional probability of the observed (or more extreme) data under H₀. Question 28. Cohen’s d is used to: A) Estimate the required sample size B) Measure effect size for mean differences C) Test for normality D) Calculate confidence intervals for proportions Answer: B Explanation: Cohen’s d standardizes the difference between two means in units of pooled standard deviation. Question 29. A 95 % confidence interval for a mean that does not contain the null‑hypothesis value of 0 suggests: A) The result is not statistically significant B) The result is statistically significant at α = 0. C) The interval is too wide to draw conclusions D) The sample size is insufficient Answer: B Explanation: If the hypothesized value lies outside the CI, we reject H₀ at the corresponding α level. Question 30. When reporting t‑test results, the conventional order of statistics is: A) t, df, p‑value B) p‑value, t, df C) df, t, p‑value
D) t, p‑value, df Answer: A Explanation: APA style typically lists the test statistic, degrees of freedom, then the p‑value. Question 31. “P‑hacking” refers to: A) Using bootstrapping to improve power B) Manipulating data or analyses to obtain significant p‑values C) Conducting a meta‑analysis D) Adjusting α after seeing the results Answer: B Explanation: P‑hacking involves questionable practices like selective reporting or multiple testing without correction. Question 32. A researcher conducts 20 independent t‑tests at α = 0.05. The probability of at least one Type I error is approximately: A) 0. B) 0. C) 0. D) 0. Answer: B Explanation: Family‑wise error ≈ 1 − (1 − 0.05)²⁰ ≈ 0.64. Question 33. Which correction method controls the family‑wise error rate by dividing α by the number of tests? A) Tukey HSD B) Bonferroni correction
B) All observed frequencies must be equal C) Sample size must be less than 30 D) Variables must be continuous Answer: A Explanation: Adequate expected frequencies ensure the chi‑square approximation is reliable. Question 37. A researcher obtains a Pearson correlation of r = 0.85 with n = 10. The test of significance will likely be: A) Non‑significant because n is too small B) Significant because the correlation is large C) Non‑significant because r cannot exceed 0.7 for n = 10 D) Significant only if α = 0. Answer: B Explanation: Even with n = 10, r = 0.85 yields a large t‑value (t = r√[(n‑2)/(1‑r²)]) and is typically significant at α = 0.05. Question 38. The term “effect size” refers to: A) The probability of a Type I error B) The magnitude of the observed effect, independent of sample size C) The sample mean difference divided by the sample size D) The p‑value of a test Answer: B Explanation: Effect size quantifies how large the effect is, separate from statistical significance. Question 39. In the context of regression, a 95 % confidence interval for β₁ that includes zero indicates:
A) The slope is significantly different from zero B) The predictor is not statistically significant at α = 0. C) Multicollinearity is present D) The model explains 100 % of variance Answer: B Explanation: If zero lies within the CI, we cannot reject H₀: β₁ = 0. Question 40. Which of the following best describes a Type II error? A) Rejecting a true null hypothesis B) Failing to reject a false null hypothesis C) Accepting the alternative hypothesis when it is false D) Using an incorrect test statistic Answer: B Explanation: A Type II error occurs when the test lacks power to detect a real effect. Question 41. Power analysis is primarily used to: A) Determine the p‑value after data collection B) Estimate the probability of a Type I error C) Calculate the required sample size to detect a specified effect D) Adjust the confidence interval width after the experiment Answer: C Explanation: Power analysis informs how many observations are needed to achieve a desired power level. Question 42. If the observed power of a test is 0.40, which statement is true?
Question 45. Which assumption is violated when the residuals of a regression model display a funnel shape? A) Linearity B) Homoscedasticity (equal variance) C) Normality of errors D) Independence of observations Answer: B Explanation: A funnel‑shaped pattern indicates heteroscedasticity, where variance changes with fitted values. Question 46. The term “degrees of freedom” in the context of a t‑test refers to: A) The number of groups being compared B) The number of independent pieces of information used to estimate variance C) The total sample size D) The number of parameters estimated in the model Answer: B Explanation: df = n − 1 for a one‑sample t‑test, reflecting how many observations are free to vary after estimating the mean. Question 47. In a repeated‑measures ANOVA, the primary source of error variance is: A) Between‑subject variability B) Within‑subject (error) variability C) Interaction between factor and subjects D) Total sum of squares Answer: B
Explanation: Repeated‑measures designs partition out subject effects, leaving within‑subject error as the main residual term. Question 48. Which test is appropriate for comparing the median of a single sample to a hypothesized value? A) One‑sample t‑test B) One‑sample sign test C) One‑sample Wilcoxon signed‑rank test D) Both B and C are acceptable, depending on symmetry assumptions Answer: D Explanation: The sign test uses only direction of differences; the Wilcoxon signed‑rank also uses magnitude, assuming symmetric distribution. Question 49. The “Bonferroni‑Holm” method is considered more powerful than the simple Bonferroni correction because: A) It increases α for all tests equally B) It applies a step‑down procedure that uses larger α thresholds for the smallest p‑values C) It controls the false discovery rate instead of family‑wise error D) It only works for independent tests Answer: B Explanation: By ordering p‑values and using progressively less stringent α, it retains more power while still controlling family‑wise error. Question 50. When the sample size is very small (n < 15) and the population variance is unknown, which test should be used for a single mean? A) Z‑test B) One‑sample t‑test with df = n − 1
C) Recommended by APA guidelines D) Irrelevant to Type I error Answer: B Explanation: Re‑labeling p‑values without a priori α inflates Type I error and is considered questionable. Question 54. In a two‑way ANOVA, an interaction effect indicates: A) The main effects are additive B) The effect of one factor depends on the level of the other factor C) There is no need for post‑hoc tests D) The error term is homogeneous Answer: B Explanation: Interaction means the influence of one independent variable changes across levels of the second. Question 55. The term “statistical significance” refers to: A) Practical importance of a finding B) The probability that the null hypothesis is true C) Evidence that an observed effect is unlikely due to random sampling alone, given α D) The size of the effect measured in standard units Answer: C Explanation: Significance assesses whether data are inconsistent with H₀ at the pre‑specified α level. Question 56. Which of the following best describes the “effect size” metric η² (eta‑squared) used in ANOVA?
A) Ratio of between‑group sum of squares to total sum of squares B) Ratio of within‑group sum of squares to total sum of squares C) Square root of R² D) Difference between group means divided by pooled SD Answer: A Explanation: η² = SS_between / SS_total, indicating proportion of total variance explained by the factor. Question 57. If a researcher conducts a one‑sample t‑test with α = 0.05 and obtains t = 2.01 with df = 15, the result is: A) Significant because t > 2 B) Not significant; critical t for df = 15 at α = 0.05 (two‑tailed) ≈ 2. C) Significant only if the test is one‑tailed D) Impossible to determine without the p‑value Answer: B Explanation: The critical two‑tailed t₀.₀₅,₁₅ ≈ 2.13; 2.01 does not exceed it, so we fail to reject H₀. Question 58. The “standard error of the difference between two means” is calculated as: A) √[(s₁²/n₁) + (s₂²/n₂)] B) (s₁ − s₂)/√(n₁ + n₂) C) (s₁ + s₂)/√(n₁ + n₂) D) √[(s₁² + s₂²)/(n₁ + n₂)] Answer: A Explanation: The SE of the difference combines the variances of each sample divided by their respective sizes.
