100 Descriptive, Inferential, and Time Series Statistics in Data Analysis - MCQs

Q: 1. Which measure of central tendency is most affected by extreme outliers?

See the full post for the detailed answer.

Q: 2. In a positively skewed distribution, the correct order of mean, median, and mode is:

See the full post for the detailed answer.

Q: 3. The interquartile range (IQR) is calculated as:

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Q: 4. Which of the following is NOT a measure of dispersion?

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Q: 5. The empirical rule applies to data that are approximately:

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Q: 6. Pearson's correlation coefficient is undefined when:

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Q: 7. Boxplot whiskers typically extend to:

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Q: 8. The coefficient of variation (CV) is useful for comparing:

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Q: 9. Z-score of a value x is given by:

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Q: 10. Chebyshev’s theorem guarantees at least what proportion within k standard deviations (k>1)?

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Category: AI & Data Science MCQDate: Published: November 8, 2025Posted by: MCQs Generator

1 min read

100 challenging multiple-choice questions on descriptive statistics, inferential methods, and time series analysis. Inspired by real data science and analytics interview questions from FAANG, consulting firms, and quant roles.

1. Which measure of central tendency is most affected by extreme outliers?

a) Median

b) Mode

c) Mean

d) Midrange

Correct Answer: c) Mean

Explanation:

The mean incorporates every value and is pulled toward extreme scores.

2. In a positively skewed distribution, the correct order of mean, median, and mode is:

a) Mean > Median > Mode

b) Mode > Median > Mean

c) Median > Mean > Mode

d) Mean > Mode > Median

Correct Answer: a) Mean > Median > Mode

Explanation:

The tail on the right pulls the mean highest, followed by median, then mode.

3. The interquartile range (IQR) is calculated as:

a) Q3 + Q1

b) Q3 – Q1

c) Q2 – Q1

d) Q3 / Q1

Correct Answer: b) Q3 – Q1

Explanation:

IQR measures spread between the 75th and 25th percentiles.

4. Which of the following is NOT a measure of dispersion?

a) Range

b) Variance

c) Kurtosis

d) Median

Correct Answer: d) Median

Explanation:

Median describes location, not spread.

5. The empirical rule applies to data that are approximately:

a) Uniformly distributed

b) Normally distributed

c) Exponentially distributed

d) Binomially distributed

Correct Answer: b) Normally distributed

Explanation:

About 68%, 95%, and 99.7% fall within 1, 2, and 3 standard deviations.

6. Pearson's correlation coefficient is undefined when:

a) Variance of X or Y is zero

b) Sample size is less than 3

c) Data are ordinal

d) Relationship is nonlinear

Correct Answer: a) Variance of X or Y is zero

Explanation:

Division by zero standard deviation makes r undefined.

7. Boxplot whiskers typically extend to:

a) Minimum and maximum values

b) 1.5 × IQR beyond Q1 and Q3

c) Mean ± 3σ

d) Q1 – Q3

Correct Answer: b) 1.5 × IQR beyond Q1 and Q3

Explanation:

Points outside are flagged as potential outliers.

8. The coefficient of variation (CV) is useful for comparing:

a) Skewness across datasets

b) Relative variability when units or means differ

c) Absolute dispersion only

d) Correlation strength

Correct Answer: b) Relative variability when units or means differ

Explanation:

CV = (σ / μ) × 100% standardizes dispersion.

9. Z-score of a value x is given by:

a) (x – μ) / σ

b) (x + μ) / σ

c) (μ – x) / σ

d) (x – median) / IQR

Correct Answer: a) (x – μ) / σ

Explanation:

Measures deviations in standard deviation units.

10. Chebyshev’s theorem guarantees at least what proportion within k standard deviations (k>1)?

a) 1 – 1/k

b) 1 – 1/k²

c) 1 – 1/(2k)

d) 1 – 2/k²

Correct Answer: b) 1 – 1/k²

Explanation:

Applies to any distribution with finite variance.

11. The sampling distribution of the sample mean becomes approximately normal when n ≥ 30 due to:

a) Law of large numbers

b) Central Limit Theorem

c) Bayes’ theorem

d) Chebyshev’s inequality

Correct Answer: b) Central Limit Theorem

Explanation:

CLT justifies normality for large samples regardless of population shape.

12. A Type I error occurs when we:

a) Fail to reject a false null

b) Reject a true null

c) Reject a false null

d) Fail to reject a true null

Correct Answer: b) Reject a true null

Explanation:

False positive; probability equals α.

13. The p-value is the probability of obtaining a test statistic at least as extreme as observed, assuming:

a) H₁ is true

b) H₀ is true

c) Sample size is large

d) Data are normal

Correct Answer: b) H₀ is true

Explanation:

Small p-value casts doubt on the null.

14. For a two-tailed z-test at α = 0.05, the critical values are:

a) ±1.645

b) ±1.96

c) ±2.33

d) ±2.58

Correct Answer: b) ±1.96

Explanation:

5% split equally in both tails.

15. The standard error of the mean is σ / √n; when σ is unknown we use:

a) Population variance

b) Sample standard deviation s

c) Median absolute deviation

d) Range / 4

Correct Answer: b) Sample standard deviation s

Explanation:

Leads to t-distribution with n–1 df.

16. Confidence interval width is proportional to:

a) 1 / √n

b) 1 / n

c) √n

d) n

Correct Answer: a) 1 / √n

Explanation:

Larger samples yield narrower intervals.

17. Power of a test = 1 – β, where β is:

a) Type I error rate

b) Type II error rate

c) Significance level

d) Confidence level

Correct Answer: b) Type II error rate

Explanation:

Probability of failing to detect a true effect.

18. For proportions, the standard error is √[p(1–p)/n]; for confidence intervals we often use:

a) Sample proportion p̂

b) Population proportion p

c) 0.5 for maximum variability

d) 1/n

Correct Answer: a) Sample proportion p̂

Explanation:

Wald interval: p̂ ± z√[p̂(1–p̂)/n].

19. The chi-square test for independence tests whether:

a) Row and column variables are associated

b) Means of two groups differ

c) Variance equals a constant

d) Data follow a normal curve

Correct Answer: a) Row and column variables are associated

Explanation:

Compares observed vs expected frequencies.

20. ANOVA tests equality of:

a) Two population means

b) Three or more population means

c) Variances across groups

d) Proportions

Correct Answer: b) Three or more population means

Explanation:

F-statistic = MSB / MSW.

21. A time series is stationary if:

a) Mean, variance, and autocovariance are time-invariant

b) Trend is linear

c) Seasonality is present

d) Data are i.i.d.

Correct Answer: a) Mean, variance, and autocovariance are time-invariant

Explanation:

Strict stationarity requires constant distribution.

22. The ACF at lag k measures:

a) Correlation between y_t and y_{t–k}

b) Variance of y_t

c) Trend strength

d) Seasonal period

Correct Answer: a) Correlation between y_t and y_{t–k}

Explanation:

Helps identify MA order.

23. In an AR(1) model y_t = φ y_{t–1} + ε_t, |φ| < 1 ensures:

a) Stationarity

b) Explosive behavior

c) Unit root

d) Seasonality

Correct Answer: a) Stationarity

Explanation:

Root outside unit circle.

24. Differencing a series once removes:

a) Linear trend

b) Constant mean

c) Seasonality of period 1

d) White noise

Correct Answer: a) Linear trend

Explanation:

Δy_t = y_t – y_{t–1} eliminates polynomial trend of order 1.

25. The PACF of an MA(1) process cuts off after:

a) Lag 1

b) Lag 2

c) Never cuts off

d) Lag 0

Correct Answer: a) Lag 1

Explanation:

Partial correlation beyond lag 1 is zero.

26. ADF test null hypothesis is:

a) Series has a unit root (non-stationary)

b) Series is stationary

c) Series has trend

d) Series is white noise

Correct Answer: a) Series has a unit root (non-stationary)

Explanation:

Reject H0 ⇒ stationary.

27. In SARIMA(p,d,q)(P,D,Q)s, 's' denotes:

a) Seasonal period

b) Differencing order

c) AR order

d) MA order

Correct Answer: a) Seasonal period

Explanation:

Common values: 12 (monthly), 4 (quarterly).

28. AIC penalizes models for:

a) Number of parameters

b) Residual variance only

c) Outliers

d) Forecast horizon

Correct Answer: a) Number of parameters

Explanation:

Lower AIC indicates better balance of fit and complexity.

29. White noise has ACF values approximately:

a) Zero for all lags > 0

b) One at lag 0, zero elsewhere

c) Decaying exponentially

d) Significant at seasonal lags

Correct Answer: a) Zero for all lags > 0

Explanation:

Uncorrelated errors.

30. Holt-Winters additive model is suitable when seasonal fluctuations:

a) Are roughly constant in size

b) Increase with the level

c) Are multiplicative

d) Are absent

Correct Answer: a) Are roughly constant in size

Explanation:

Multiplicative version for proportional seasonality.

31. The variance of a dataset {2, 4, 6, 8, 10} is:

a) 6

b) 8

c) 10

d) 12

Correct Answer: b) 8

Explanation:

Mean = 6; variance = [(−4)² + (−2)² + 0 + 2² + 4²]/4 = 40/5 = 8.

32. For the data {1, 3, 3, 6}, the mode is:

a) 1

b) 3

c) 6

d) Bimodal

Correct Answer: b) 3

Explanation:

3 appears twice; others once.

33. Skewness coefficient > 0 indicates:

a) Symmetric distribution

b) Left-skewed

c) Right-skewed

d) Platykurtic

Correct Answer: c) Right-skewed

Explanation:

Longer tail on the positive side.

34. Percentile rank of the median is:

a) 25th

b) 50th

c) 75th

d) 100th

Correct Answer: b) 50th

Explanation:

Half the data lie below the median.

35. Geometric mean is preferred for:

a) Averaging rates of change

b) Additive data

c) Nominal variables

d) Counts

Correct Answer: a) Averaging rates of change

Explanation:

Handles compounding/multiplicative processes.

36. Covariance of a variable with itself equals its:

a) Variance

b) Standard deviation

c) Mean

d) Range

Correct Answer: a) Variance

Explanation:

Cov(X,X) = Var(X).

37. Spearman’s rank correlation is based on:

a) Original values

b) Ranks of the data

c) Deviations from mean

d) Log-transformed values

Correct Answer: b) Ranks of the data

Explanation:

Non-parametric measure of monotonic relationship.

38. The 95% CI for μ when n=25, x̄=50, s=10 (t-critical ≈ 2.064) is:

a) 50 ± 4.13

b) 50 ± 3.92

c) 50 ± 2.06

d) 50 ± 1.96

Correct Answer: a) 50 ± 4.13

Explanation:

Margin = 2.064 × (10/√25) = 2.064 × 2 ≈ 4.13.

39. A test statistic z = 2.5, α = 0.01 two-tailed; decision is:

a) Reject H0

b) Fail to reject H0

c) p = 0.0124

d) Need df

Correct Answer: b) Fail to reject H0

Explanation:

Critical |z| = 2.576 > 2.5.

40. Minimum sample size for proportion CI with margin of error E=0.03, p*=0.5, z=1.96:

a) 1068

b) 752

c) 385

d) 267

Correct Answer: a) 1068

Explanation:

n = (1.96² × 0.5 × 0.5) / 0.03² ≈ 1067.11 → 1068.

41. For paired t-test, degrees of freedom =

a) n₁ + n₂ – 2

b) n – 1

c) 2n – 1

d) n

Correct Answer: b) n – 1

Explanation:

Based on differences (n pairs).

42. F-test is used to compare:

a) Two variances

b) Two means

c) Proportions

d) Correlations

Correct Answer: a) Two variances

Explanation:

H0: σ₁² = σ₂².

43. Mann-Whitney U tests difference in:

a) Medians of two independent samples

b) Means of paired data

c) Variances

d) Proportions

Correct Answer: a) Medians of two independent samples

Explanation:

Non-parametric alternative to two-sample t-test.

44. Kruskal-Wallis is the non-parametric version of:

a) One-way ANOVA

b) Paired t-test

c) Chi-square goodness-of-fit

d) Linear regression

Correct Answer: a) One-way ANOVA

Explanation:

Compares three or more independent groups.

45. The Durbin-Watson statistic near 2 indicates:

a) No autocorrelation

b) Positive autocorrelation

c) Negative autocorrelation

d) Heteroscedasticity

Correct Answer: a) No autocorrelation

Explanation:

Range 0–4; 2 is ideal.

46. In exponential smoothing, α close to 1 gives more weight to:

a) Recent observations

b) Older observations

c) Seasonal component

d) Trend

Correct Answer: a) Recent observations

Explanation:

Higher α reacts faster to changes.

47. An AR(2) model requires PACF significant at:

a) Lags 1 and 2

b) Lag 1 only

c) All lags

d) Lag 2 only

Correct Answer: a) Lags 1 and 2

Explanation:

PACF cuts off after p.

48. Seasonal differencing of period 12 is denoted as:

a) ∇₁₂ y_t

b) ∇ y_t

c) log y_t

d) y_t – y_{t–1}

Correct Answer: a) ∇₁₂ y_t

Explanation:

∇₁₂ y_t = y_t – y_{t–12}.

49. Ljung-Box test checks for:

a) Lack of autocorrelation in residuals

b) Normality

c) Stationarity

d) Homoscedasticity

Correct Answer: a) Lack of autocorrelation in residuals

Explanation:

High p-value supports white noise.

50. KPSS test null hypothesis is:

a) Stationarity

b) Unit root

c) Trend

d) Seasonality

Correct Answer: a) Stationarity

Explanation:

Complements ADF; fail to reject ⇒ stationary.

51. In ARIMA, 'I' stands for:

a) Integrated

b) Invertible

c) Independent

d) Intercept

Correct Answer: a) Integrated

Explanation:

Order of differencing to achieve stationarity.

52. Forecasts from a random walk model are:

a) Last observed value

b) Mean of series

c) Zero

d) Trend line

Correct Answer: a) Last observed value

Explanation:

y_{t+1} = y_t + ε_{t+1} ⇒ best forecast = y_t.

53. Granger causality tests whether past values of X improve prediction of:

a) Y beyond its own past

b) X itself

c) Error term

d) Trend

Correct Answer: a) Y beyond its own past

Explanation:

Rejects non-causality if X lags are significant in Y equation.

54. Variance inflation factor (VIF) > 10 suggests:

a) Severe multicollinearity

b) Heteroscedasticity

c) Autocorrelation

d) Non-normality

Correct Answer: a) Severe multicollinearity

Explanation:

VIF_j = 1 / (1 – R_j²).

55. The coefficient of determination R² represents:

a) Proportion of variance explained

b) Correlation coefficient

c) Slope of regression

d) p-value

Correct Answer: a) Proportion of variance explained

Explanation:

SSR / SST.

56. In simple linear regression, the least squares slope b1 =

a) Cov(X,Y) / Var(X)

b) Cov(X,Y) / Var(Y)

c) Mean(Y) / Mean(X)

d) SD(Y) / SD(X)

Correct Answer: a) Cov(X,Y) / Var(X)

Explanation:

Minimizes sum of squared residuals.

57. Residual standard error estimates:

a) σ, the error standard deviation

b) β0

c) R²

d) F-statistic

Correct Answer: a) σ, the error standard deviation

Explanation:

√(SSE / (n–2)).

58. For logistic regression, the link function is:

a) Logit

b) Probit

c) Log

d) Identity

Correct Answer: a) Logit

Explanation:

log(p/(1–p)) = β0 + β1x.

59. The odds ratio exp(β) = 1.5 means:

a) 50% increase in odds per unit increase in x

b) 1.5 times the probability

c) Log odds increase by 1.5

d) Probability increases by 0.5

Correct Answer: a) 50% increase in odds per unit increase in x

Explanation:

Odds multiply by exp(β).

60. Poisson regression is suitable for:

a) Count data

b) Binary outcomes

c) Continuous positive data

d) Time to event

Correct Answer: a) Count data

Explanation:

Mean = variance.

61. In survival analysis, Kaplan-Meier estimates:

a) Survival function non-parametrically

b) Hazard ratio

c) Median survival time only

d) Proportional hazards

Correct Answer: a) Survival function non-parametrically

Explanation:

Product-limit estimator handles censoring.

62. Cox proportional hazards assumption is violated if:

a) Hazard ratios change over time

b) Log(-log(S(t))) curves are parallel

c) Schoenfeld residuals show no trend

d) p-value < 0.05

Correct Answer: a) Hazard ratios change over time

Explanation:

Check via time-dependent covariates or plots.

63. Bayesian inference updates beliefs using:

a) Prior × Likelihood → Posterior

b) Likelihood only

c) Posterior × Data

d) Prior / Likelihood

Correct Answer: a) Prior × Likelihood → Posterior

Explanation:

Bayes’ theorem: P(θ|data) ∝ P(data|θ) P(θ).

64. Conjugate prior for normal mean (known variance) is:

a) Normal

b) Gamma

c) Beta

d) Inverse-gamma

Correct Answer: a) Normal

Explanation:

Posterior remains normal.

65. MCMC methods are used to:

a) Sample from complex posterior distributions

b) Compute exact integrals

c) Perform hypothesis tests

d) Calculate p-values

Correct Answer: a) Sample from complex posterior distributions

Explanation:

Markov Chain Monte Carlo approximates posteriors.

66. Bootstrapping estimates sampling distribution by:

a) Resampling with replacement from the data

b) Using parametric assumptions

c) Increasing sample size

d) Theoretical formulas

Correct Answer: a) Resampling with replacement from the data

Explanation:

Non-parametric; empirical distribution.

67. Percentile bootstrap CI uses:

a) 2.5th and 97.5th percentiles of bootstrap statistics

b) Mean ± 1.96 SE

c) t-distribution

d) Chi-square

Correct Answer: a) 2.5th and 97.5th percentiles of bootstrap statistics

Explanation:

For 95% CI from B=1000 replicates.

68. Cross-validation is primarily used to assess:

a) Model generalization error

b) p-values

c) Confidence intervals

d) Residual normality

Correct Answer: a) Model generalization error

Explanation:

K-fold CV estimates out-of-sample performance.

69. The bias-variance tradeoff implies that overly complex models tend to:

a) Overfit (high variance, low bias)

b) Underfit (high bias, low variance)

c) Balance perfectly

d) Have zero error

Correct Answer: a) Overfit (high variance, low bias)

Explanation:

Capture noise, not just signal.

70. Principal Component Analysis (PCA) maximizes:

a) Variance along projected directions

b) Correlation between variables

c) Mean squared error

d) Entropy

Correct Answer: a) Variance along projected directions

Explanation:

Eigenvectors of covariance matrix.

71. The scree plot helps determine number of PCs by looking for:

a) Elbow in eigenvalue decline

b) Linear trend

c) Constant variance

d) Zero eigenvalues

Correct Answer: a) Elbow in eigenvalue decline

Explanation:

Retain components before sharp drop.

72. In k-means clustering, the objective is to minimize:

a) Within-cluster sum of squares

b) Between-cluster sum of squares

c) Total sum of squares

d) Silhouette score

Correct Answer: a) Within-cluster sum of squares

Explanation:

Iterative assignment and centroid update.

73. Silhouette coefficient ranges from:

a) –1 to +1

b) 0 to 1

c) –∞ to +∞

d) 0 to ∞

Correct Answer: a) –1 to +1

Explanation:

Higher values indicate better cluster separation.

74. A contingency table with all expected frequencies ≥ 5 is required for:

a) Chi-square test validity

b) t-test

c) ANOVA

d) Regression

Correct Answer: a) Chi-square test validity

Explanation:

Approximation to chi-square distribution.

75. McNemar’s test is used for:

a) Paired binary data

b) Independent proportions

c) Continuous paired data

d) Multiple groups

Correct Answer: a) Paired binary data

Explanation:

Tests marginal homogeneity.

76. The central limit theorem requires random samples that are:

a) Independent and identically distributed

b) Normally distributed

c) Paired

d) Stratified

Correct Answer: a) Independent and identically distributed

Explanation:

For large n, sample mean ≈ normal.

77. Degrees of freedom for two-sample t-test (unequal variances) is approximately:

a) Welch-Satterthwaite formula

b) n1 + n2 – 1

c) n1 + n2 – 2

d) min(n1, n2) – 1

Correct Answer: a) Welch-Satterthwaite formula

Explanation:

Conservative; avoids equal variance assumption.

78. Effect size Cohen’s d = (μ1 – μ2) / σ; d = 0.8 is considered:

a) Large

b) Medium

c) Small

d) Negligible

Correct Answer: a) Large

Explanation:

Benchmarks: 0.2 small, 0.5 medium, 0.8 large.

79. Multiple R² in regression can be artificially inflated by:

a) Adding irrelevant predictors

b) Removing outliers

c) Transforming variables

d) Increasing sample size

Correct Answer: a) Adding irrelevant predictors

Explanation:

Use adjusted R² to penalize extra terms.

80. Homoscedasticity means residuals have:

a) Constant variance across predicted values

b) Zero mean

c) Normal distribution

d) No autocorrelation

Correct Answer: a) Constant variance across predicted values

Explanation:

Breusch-Pagan test checks this.

81. Durbin-Watson values < 1 typically indicate:

a) Strong positive autocorrelation

b) No autocorrelation

c) Negative autocorrelation

d) Heteroscedasticity

Correct Answer: a) Strong positive autocorrelation

Explanation:

Values near 0 = positive; near 4 = negative.

82. In time series decomposition, the remainder after trend and seasonal removal is:

a) Irregular (random) component

b) Cyclical component

c) Trend

d) Seasonal index

Correct Answer: a) Irregular (random) component

Explanation:

Should resemble white noise if model is good.

83. STL decomposition stands for:

a) Seasonal-Trend decomposition using LOESS

b) Simple Time Series Linear

c) Standard Trend Line

d) Smooth Time Lag

Correct Answer: a) Seasonal-Trend decomposition using LOESS

Explanation:

Robust, flexible for varying seasonal patterns.

84. ACF of a seasonal series with period 12 shows spikes at:

a) Multiples of 12

b) Lag 1 only

c) All lags

d) Lag 0

Correct Answer: a) Multiples of 12

Explanation:

Indicates need for seasonal AR/MA terms.

85. Box-Cox transformation is applied to stabilize:

a) Variance (heteroscedasticity)

b) Mean

c) Trend

d) Seasonality

Correct Answer: a) Variance (heteroscedasticity)

Explanation:

y(λ) = (y^λ – 1)/λ or log(y) for λ=0.

86. Over-differencing a stationary series introduces:

a) MA(1) structure with negative coefficient

b) Unit root

c) Trend

d) Seasonality

Correct Answer: a) MA(1) structure with negative coefficient

Explanation:

ACF shows spike at lag 1, then near zero.

87. The optimal ARIMA model often has residuals with:

a) No significant ACF/PACF spikes (white noise)

b) Significant lag 1

c) Linear trend

d) Seasonal pattern

Correct Answer: a) No significant ACF/PACF spikes (white noise)

Explanation:

Ljung-Box p > 0.05 supports adequacy.

88. In VAR models, each variable is modeled as a function of:

a) Its own lags and lags of all other variables

b) Only its own lags

c) Exogenous variables

d) Trend only

Correct Answer: a) Its own lags and lags of all other variables

Explanation:

Vector autoregression for multivariate time series.

89. Impulse response function traces effect of a shock in one variable on:

a) Future values of all variables

b) Past values

c) Error term

d) Constant term

Correct Answer: a) Future values of all variables

Explanation:

Shows dynamic responses in VAR.

90. Cointegration means two non-stationary series have:

a) A stationary linear combination

b) Identical trends

c) Zero correlation

d) Same variance

Correct Answer: a) A stationary linear combination

Explanation:

Long-run equilibrium relationship.

91. Johansen test is used to detect:

a) Number of cointegrating relationships

b) Unit roots

c) Granger causality

d) ARCH effects

Correct Answer: a) Number of cointegrating relationships

Explanation:

Trace and max-eigenvalue statistics.

92. ARCH model tests for:

a) Time-varying volatility (heteroscedasticity)

b) Mean reversion

c) Trend

d) Seasonality

Correct Answer: a) Time-varying volatility (heteroscedasticity)

Explanation:

Variance depends on past squared errors.

93. GARCH(1,1) models volatility as:

a) σ²_t = α₀ + α₁ ε²_{t–1} + β₁ σ²_{t–1}

b) σ_t = α₀ + α₁ |ε_{t–1}|

c) σ_t = constant

d) σ²_t = ε²_{t–1}

Correct Answer: a) σ²_t = α₀ + α₁ ε²_{t–1} + β₁ σ²_{t–1}

Explanation:

Combines ARCH and persistence.

94. The Jarque-Bera test assesses:

a) Normality of residuals (skewness + kurtosis)

b) Autocorrelation

c) Stationarity

d) Homoscedasticity

Correct Answer: a) Normality of residuals (skewness + kurtosis)

Explanation:

JB statistic ~ χ²(2).

95. Shapiro-Wilk test null hypothesis is:

a) Data come from a normal distribution

b) Data are skewed

c) Variance is constant

d) Mean equals zero

Correct Answer: a) Data come from a normal distribution

Explanation:

Powerful for small samples.

96. Levene’s test checks for:

a) Equality of variances across groups

b) Equality of means

c) Normality

d) Independence

Correct Answer: a) Equality of variances across groups

Explanation:

Robust to non-normality.

97. The Bonferroni correction adjusts α by:

a) Dividing by number of tests

b) Multiplying by number of tests

c) Using α/2

d) Square root

Correct Answer: a) Dividing by number of tests

Explanation:

Controls family-wise error rate conservatively.

98. Holm’s method is a:

a) Step-down multiple comparison procedure

b) Parametric test

c) Non-parametric ANOVA

d) Bayesian test

Correct Answer: a) Step-down multiple comparison procedure

Explanation:

Less conservative than Bonferroni.

99. Tukey’s HSD test is used after ANOVA to compare:

a) All pairwise means

b) Means vs control

c) Variances

d) Medians

Correct Answer: a) All pairwise means

Explanation:

Honest Significant Difference; assumes equal variances.

100. Dunnett’s test compares:

a) Multiple treatments vs a single control

b) All pairs

c) Proportions

d) Correlations

Correct Answer: a) Multiple treatments vs a single control

Explanation:

Fewer comparisons, higher power.

101. The Q-Q plot assesses normality by plotting:

a) Sample quantiles vs theoretical normal quantiles

b) Residuals vs fitted

c) ACF

d) Histogram

Correct Answer: a) Sample quantiles vs theoretical normal quantiles

Explanation:

Straight line indicates normality.

102. A leverage point in regression has high:

a) Distance from mean of X (hat diagonal)

b) Residual

c) Cook’s distance

d) Standardized coefficient

Correct Answer: a) Distance from mean of X (hat diagonal)

Explanation:

h_ii > 2p/n flags potential leverage.

103. Cook’s distance measures:

a) Influence of an observation on all fitted values

b) Residual size

c) Multicollinearity

d) Heteroscedasticity

Correct Answer: a) Influence of an observation on all fitted values

Explanation:

Large values (> 4/n) indicate influential points.

104. The partial F-test in regression compares:

a) Nested models (reduced vs full)

b) Two independent samples

c) Variances

d) Proportions

Correct Answer: a) Nested models (reduced vs full)

Explanation:

Tests significance of added predictors.

105. Ridge regression adds penalty:

a) λ Σ β_j² (L2)

b) λ Σ |β_j| (L1)

c) λ Σ (β_j – 1)²

d) No penalty

Correct Answer: a) λ Σ β_j² (L2)

Explanation:

Shrinks coefficients, handles multicollinearity.

106. Lasso can perform variable selection because it:

a) Sets some coefficients exactly to zero

b) Shrinks all equally

c) Increases variance

d) Removes intercept

Correct Answer: a) Sets some coefficients exactly to zero

Explanation:

L1 penalty promotes sparsity.

107. Elastic Net combines:

a) Ridge and Lasso penalties

b) Ridge and OLS

c) Lasso and PCR

d) PCR and PLS

Correct Answer: a) Ridge and Lasso penalties

Explanation:

Useful when p > n or high correlation.

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100 Descriptive, Inferential, and Time Series Statistics in Data Analysis - MCQs

1. Which measure of central tendency is most affected by extreme outliers?

2. In a positively skewed distribution, the correct order of mean, median, and mode is:

3. The interquartile range (IQR) is calculated as:

4. Which of the following is NOT a measure of dispersion?

5. The empirical rule applies to data that are approximately:

6. Pearson's correlation coefficient is undefined when:

7. Boxplot whiskers typically extend to:

8. The coefficient of variation (CV) is useful for comparing:

9. Z-score of a value x is given by:

10. Chebyshev’s theorem guarantees at least what proportion within k standard deviations (k>1)?

11. The sampling distribution of the sample mean becomes approximately normal when n ≥ 30 due to:

12. A Type I error occurs when we:

13. The p-value is the probability of obtaining a test statistic at least as extreme as observed, assuming:

14. For a two-tailed z-test at α = 0.05, the critical values are:

15. The standard error of the mean is σ / √n; when σ is unknown we use:

16. Confidence interval width is proportional to:

17. Power of a test = 1 – β, where β is:

18. For proportions, the standard error is √[p(1–p)/n]; for confidence intervals we often use:

19. The chi-square test for independence tests whether:

20. ANOVA tests equality of:

21. A time series is stationary if:

22. The ACF at lag k measures:

23. In an AR(1) model y_t = φ y_{t–1} + ε_t, |φ| < 1 ensures:

24. Differencing a series once removes:

25. The PACF of an MA(1) process cuts off after:

26. ADF test null hypothesis is:

27. In SARIMA(p,d,q)(P,D,Q)s, 's' denotes:

28. AIC penalizes models for:

29. White noise has ACF values approximately:

30. Holt-Winters additive model is suitable when seasonal fluctuations:

31. The variance of a dataset {2, 4, 6, 8, 10} is:

32. For the data {1, 3, 3, 6}, the mode is:

33. Skewness coefficient > 0 indicates:

34. Percentile rank of the median is:

35. Geometric mean is preferred for:

36. Covariance of a variable with itself equals its:

37. Spearman’s rank correlation is based on:

38. The 95% CI for μ when n=25, x̄=50, s=10 (t-critical ≈ 2.064) is:

39. A test statistic z = 2.5, α = 0.01 two-tailed; decision is:

40. Minimum sample size for proportion CI with margin of error E=0.03, p*=0.5, z=1.96:

41. For paired t-test, degrees of freedom =

42. F-test is used to compare:

43. Mann-Whitney U tests difference in:

44. Kruskal-Wallis is the non-parametric version of:

45. The Durbin-Watson statistic near 2 indicates:

46. In exponential smoothing, α close to 1 gives more weight to:

47. An AR(2) model requires PACF significant at:

48. Seasonal differencing of period 12 is denoted as:

49. Ljung-Box test checks for:

50. KPSS test null hypothesis is:

51. In ARIMA, 'I' stands for:

52. Forecasts from a random walk model are:

53. Granger causality tests whether past values of X improve prediction of:

54. Variance inflation factor (VIF) > 10 suggests:

55. The coefficient of determination R² represents:

56. In simple linear regression, the least squares slope b1 =

57. Residual standard error estimates:

58. For logistic regression, the link function is:

59. The odds ratio exp(β) = 1.5 means:

60. Poisson regression is suitable for:

61. In survival analysis, Kaplan-Meier estimates:

62. Cox proportional hazards assumption is violated if:

63. Bayesian inference updates beliefs using:

64. Conjugate prior for normal mean (known variance) is:

65. MCMC methods are used to:

66. Bootstrapping estimates sampling distribution by:

67. Percentile bootstrap CI uses:

68. Cross-validation is primarily used to assess:

69. The bias-variance tradeoff implies that overly complex models tend to:

70. Principal Component Analysis (PCA) maximizes:

71. The scree plot helps determine number of PCs by looking for:

72. In k-means clustering, the objective is to minimize:

73. Silhouette coefficient ranges from:

74. A contingency table with all expected frequencies ≥ 5 is required for:

75. McNemar’s test is used for:

76. The central limit theorem requires random samples that are:

77. Degrees of freedom for two-sample t-test (unequal variances) is approximately:

78. Effect size Cohen’s d = (μ1 – μ2) / σ; d = 0.8 is considered: