HAT Subject (Statistics) FLP 1 Free Quiz

HAT Subject (Statistics) – FLP 1

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HAT Subject (Statistics) – FLP 1 consists of 100 MCQs covering 1 subjects. You have 120 minutes to complete it. Start with the easier questions and manage your time wisely. Good luck!

Statistics 100 MCQs

1. What does descriptive statistics do?

A. Summarizes and describes data B. Inferential statistics C. Predictive statistics D. Prescriptive statistics

2. What is the most frequent value in a dataset?

A. Mean B. Mode C. Median D. Range

3. What measures the spread of data around the mean?

A. Standard deviation B. Range C. Variance D. Interquartile range

4. What plot shows the relationship between two numerical variables?

A. Histogram B. Bar chart C. Pie chart D. Scatter plot

5. What measures how many standard deviations a value is from the mean?

A. Percentile B. Z-score C. Quartile D. Decile

6. What measures the strength and direction of a linear relationship?

A. Covariance B. Regression C. Correlation coefficient D. Causation

7. What plot displays data while preserving individual values?

A. Histogram B. Stem-and-leaf plot C. Box plot D. Scatter plot

8. What variable is manipulated by the experimenter?

A. Dependent B. Control C. Independent D. Confounding

9. What variable is measured to determine the effect?

A. Manipulated B. Control C. Independent D. Dependent

10. What design assigns subjects to treatments randomly?

A. Randomized block B. Latin square C. Completely randomized D. Factorial

11. What design is used when some factors are hard to change?

A. CRD B. Randomized block C. Latin square D. Split-plot

12. What design has all combinations of factor levels?

A. Crossed B. Nested C. Split-plot D. Latin square

13. What is the assignment of treatments to experimental units by chance?

A. Replication B. Blocking C. Confounding D. Randomization

14. What is the grouping of experimental units to control variability?

A. Randomization B. Blocking C. Replication D. Confounding

15. What occurs when the effects of factors cannot be separated?

A. Confounding B. Randomization C. Blocking D. Replication

16. What compares the between-group variance to the within-group variance?

A. t-test B. F-test C. Chi-square D. z-test

17. What ANOVA has one factor with multiple levels?

A. One-way B. Two-way C. Three-way D. Factorial

18. What test checks the homogeneity of variances assumption?

A. Shapiro-Wilk B. Levene's C. Durbin-Watson D. Breusch-Pagan

19. What test checks the normality assumption?

A. Shapiro-Wilk B. Levene's C. Durbin-Watson D. Breusch-Pagan

20. What does a small p-value indicate?

A. Large B. Zero C. Small D. Negative

21. What is the probability of rejecting a false null hypothesis?

A. Significance level B. P-value C. Confidence level D. Power

22. Which test is used for small samples with unknown variance?

A. z-test B. Chi-square C. F-test D. t-test

23. What is the range of values for which H0 is rejected?

A. Rejection region B. Acceptance region C. Confidence interval D. P-value

24. What can be used for hypothesis testing by checking if the parameter value is included?

A. P-value B. Test statistic C. Confidence interval D. Rejection region

25. What is another method for hypothesis testing?

A. Score B. Wald C. Likelihood ratio D. F

26. What is a measure of effect size for factorial ANOVA?

A. Eta-squared B. Omega-squared C. Partial eta-squared D. Cohen's d

27. What is a multivariate extension of ANOVA?

A. Hotelling B. Discriminant C. MANOVA D. PCA

28. What measures the relationship between two sets of variables?

A. PCA B. Factor C. Discriminant D. Canonical correlation

29. What represent the variance explained by each component in PCA?

A. Eigenvectors B. Loadings C. Scores D. Eigenvalues

30. What is used to evaluate clustering quality?

A. Elbow B. Silhouette C. Inertia D. Gap statistic

31. What is used to determine the optimal number of clusters?

A. Elbow method B. Silhouette C. Gap statistic D. Inertia

32. What is another method for determining the number of clusters?

A. Elbow B. Silhouette C. Gap statistic D. Inertia

33. What is the dimension of a matrix's column space?

A. Rank B. Trace C. Determinant D. Norm

34. What is a measure of a matrix's size?

A. Trace B. Determinant C. Norm D. Rank

35. What do probability distributions describe?

A. Likelihood of different outcomes B. Descriptive statistics C. Sampling techniques D. Regression models

36. What are the parameters of the binomial distribution?

A. μ and σ B. λ C. α and β D. n and p

37. What distribution models the number of events in a fixed interval?

A. Binomial B. Poisson C. Normal D. Exponential

38. What are the parameters of the normal distribution?

A. n and p B. λ C. α and β D. μ and σ

39. What are the mean and standard deviation of the standard normal distribution?

A. Mean 1, SD 0 B. Mean 0, SD 1 C. Mean 0, SD 0 D. Mean 1, SD 1

40. What distribution has constant probability over an interval?

A. Uniform B. Normal C. Exponential D. Binomial

41. What is the parameter of the exponential distribution?

A. n and p B. μ and σ C. α and β D. λ

42. Which distribution is used for small samples when the variance is unknown?

A. Normal B. t C. Chi-square D. F

43. Which distribution is used for variance tests?

A. Chi-square B. t C. F D. Normal

44. Which distribution is used in ANOVA?

A. t B. Chi-square C. F D. Normal

45. What distribution models the number of failures before a specified number of successes?

A. Binomial B. Negative binomial C. Poisson D. Geometric

46. What is the Fourier transform of a distribution?

A. MGF B. CGF C. Characteristic function D. PGF

47. Which generating function is used for discrete distributions?

A. MGF B. PGF C. CGF D. Characteristic function

48. What is the shape of the normal distribution?

A. Symmetric B. Skewed right C. Skewed left D. Bimodal

49. What is a process with uncertain outcomes called?

A. Deterministic B. Predictable C. Certain D. Random experiment

50. What function gives P(X ≤ x)?

A. PMF B. PDF C. CDF D. MGF

51. What is the standard deviation?

A. Square root of variance B. Variance C. Mean D. Covariance

52. What inequality bounds the probability of deviation from the mean?

A. Markov B. Chebyshev C. Jensen D. Cauchy-Schwarz

53. What is regression analysis?

A. Modeling relationships between variables B. Classification C. Clustering D. Association

54. What is the equation of a simple linear regression line?

A. y = b0 + b1x + ε B. y = b0 + b1x^2 C. y = b0 + b1x + b2x^2 D. y = b0 + b1x

55. What measures the proportion of variance explained by the model?

A. Correlation B. Slope C. Intercept D. R²

56. What is the range of R²?

A. -1 to 1 B. 0 to 1 C. 0 to ∞ D. -∞ to ∞

57. What penalizes the addition of unnecessary predictors?

A. Adjusted R² B. R² C. Correlation D. AIC

58. What are the differences between observed and predicted values?

A. Errors B. Coefficients C. Residuals D. Intercepts

59. What does the Durbin-Watson test detect?

A. Heteroskedasticity B. Multicollinearity C. Normality D. Autocorrelation

60. What occurs when independent variables are highly correlated?

A. Multicollinearity B. Heteroskedasticity C. Autocorrelation D. Non-normality

61. What detects multicollinearity?

A. Durbin-Watson B. Breusch-Pagan C. VIF D. Shapiro-Wilk

62. What does a high VIF indicate?

A. Low B. Zero C. Negative D. High

63. What test checks for normality of residuals?

A. Shapiro-Wilk B. Durbin-Watson C. Breusch-Pagan D. VIF

64. Which regression is used when the dependent variable is binary?

A. Linear B. Polynomial C. Logistic D. Multiple

65. What regression models the relationship between a dependent variable and multiple independent variables?

A. Simple B. Multiple C. Logistic D. Polynomial

66. What tests the overall significance of the regression model?

A. F-test B. t-test C. Chi-square D. z-test

67. Which regularization method adds a penalty to the coefficients?

A. Lasso B. Ridge C. Elastic net D. Stepwise

68. What measures the influence of each observation in regression?

A. Cook's distance B. Leverage C. DFFITS D. DFBETAS

69. What is the basic form of random sampling?

A. Stratified B. Simple random C. Cluster D. Systematic

70. What sampling method divides the population into homogeneous subgroups?

A. Stratified B. Cluster C. Systematic D. Simple random

71. What is the list of all individuals in the population from which the sample is drawn?

A. Sample B. Population C. Stratum D. Sampling frame

72. What affects the precision of estimates?

A. Sample frame B. Sampling method C. Sample size D. Population size

73. What is the sample size formula for a mean?

A. (z² σ²)/E² B. (z² p q)/E² C. (z σ/E)^2 D. (t σ/E)^2

74. What allocation minimizes the variance for a fixed sample size?

A. Proportional B. Neyman C. Equal D. Optimal

75. What adjusts the standard error when sampling without replacement from a finite population?

A. Finite population correction B. Sample fraction C. Population size D. Sample size

76. What means that each individual can be selected only once?

A. With replacement B. Stratified C. Without replacement D. Cluster

77. What is a resampling method that leaves out one observation at a time?

A. Jackknife B. Bootstrap C. Cross-validation D. Permutation

78. What is a resampling method used to assess model performance?

A. Bootstrap B. Jackknife C. Cross-validation D. Permutation

79. What is a numerical characteristic of a sample?

A. Statistic B. Parameter C. Population D. Variable

80. What is the standard deviation of a sampling distribution?

A. Population standard deviation B. Sample standard deviation C. Variance D. Standard error

81. What is an interval estimate with a specified confidence level?

A. Point estimate B. Margin of error C. Confidence interval D. Standard error

82. What is the probability that the confidence interval contains the true parameter?

A. Significance level B. P-value C. Power D. Confidence level

83. What is the half-width of a confidence interval?

A. Standard error B. Margin of error C. Confidence level D. P-value

84. What states that the sample mean converges to the population mean?

A. CLT B. Bayes C. Law of large numbers D. Markov

85. What theorem provides a way to improve an estimator using a sufficient statistic?

A. Rao-Blackwell B. Cramer-Rao C. Lehmann-Scheffe D. Fisher-Neyman

86. What theorem states that the MVUE is a function of a complete sufficient statistic?

A. Rao-Blackwell B. Cramer-Rao C. Lehmann-Scheffe D. Fisher-Neyman

87. What is the joint probability of the data given the parameter?

A. Prior B. Likelihood C. Posterior D. Marginal

88. What method finds the parameter value that maximizes the likelihood function?

A. MLE B. Method of moments C. Least squares D. Bayesian

89. What method estimates parameters by equating sample moments to population moments?

A. MLE B. Bayesian C. Method of moments D. Least squares

90. What uses prior and likelihood to obtain a posterior distribution?

A. MLE B. Method of moments C. Least squares D. Bayesian

91. What is a sequence of observations ordered by time?

A. Cross-sectional B. Panel C. Time series D. Experimental

92. What is a long-term increase or decrease in a time series?

A. Seasonality B. Cyclical C. Irregular D. Trend

93. What are fluctuations that occur over longer periods without fixed frequency?

A. Cyclical B. Seasonality C. Trend D. Irregular

94. What is the correlation between a time series and its lagged values?

A. Cross-correlation B. Partial autocorrelation C. Correlation D. Autocorrelation

95. What means the statistical properties are constant over time?

A. Non-stationarity B. Seasonality C. Stationarity D. Trend

96. What model extends ARIMA to include seasonal components?

A. AR B. SARIMA C. MA D. ARMA

97. What is used for model selection in time series analysis?

A. BIC B. AIC C. R² D. Adjusted R²

98. What is a simple smoothing technique?

A. Exponential smoothing B. Moving average C. ARIMA D. Regression

99. What is the difference between the actual and predicted values?

A. Forecast error B. Residual C. Residual D. Error

100. What is another measure of forecast accuracy?

A. MAE B. MAPE C. MASE D. RMSE

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