Sample Questions and Answers
The “p-value” helps to assess the evidence against:
A. The null hypothesis.
B. The alternative hypothesis.
C. The sample mean.
D. The variance of the data.
Answer: A
The “Chi-square goodness-of-fit test” is used to determine if:
A. There is a significant difference between the means of two groups.
B. The observed distribution of a categorical variable fits the expected distribution.
C. There is a correlation between two variables.
D. The data follows a normal distribution.
Answer: B
In time series analysis, “trend analysis” is used to:
A. Examine the long-term movement or direction of the data.
B. Analyze short-term fluctuations in the data.
C. Model the seasonal component of the data.
D. Identify outliers in the data.
Answer: A
In hypothesis testing, the “power of the test” refers to:
The probability of rejecting the null hypothesis when it is true.
B. The probability of not making a Type I error.
C. The probability of correctly rejecting the null hypothesis when it is false.
D. The probability of making a Type II error.
Answer: C
“Z-scores” are used to:
Convert raw data values into standard deviations from the mean.
B. Normalize data to a 0-1 scale.
C. Test for the normality of data.
D. Estimate the variance of the population.
Answer: A
The “central limit theorem” states that:
The sample mean follows a normal distribution, regardless of the population distribution.
B. The sum of a sample will always follow a uniform distribution.
C. The population mean can be estimated using the sample median.
D. The variance of the sample will always be equal to the variance of the population.
Answer: A
In decision theory, the “certainty equivalent” is:
The maximum amount of money that an individual would be willing to pay to avoid risk.
B. The amount of money that an individual would accept with certainty, as an alternative to a risky decision.
C. The expected value of a decision under uncertainty.
D. The best possible payoff in a decision tree.
Answer: B
In regression analysis, the “F-statistic” is used to:
Test the significance of individual regression coefficients.
B. Test whether at least one of the independent variables significantly explains the variation in the dependent variable.
C. Calculate the strength of the correlation between two variables.
D. Estimate the residual sum of squares.
Answer: B
In hypothesis testing, the “p-value” represents:
The probability of the null hypothesis being true.
B. The probability of observing the sample data given that the null hypothesis is true.
C. The probability that the alternative hypothesis is correct.
D. The probability of rejecting the alternative hypothesis.
Answer: B
The “method of least squares” in regression analysis is used to:
Minimize the sum of squared residuals.
B. Maximize the sum of squared residuals.
C. Minimize the correlation between the independent variables.
D. Maximize the total variance explained by the model.
Answer: A
In decision theory, the “maximin” criterion is applied when:
A decision-maker is risk-neutral.
B. A decision-maker prefers to maximize the best possible outcome.
C. A decision-maker seeks to minimize the worst possible loss.
D. A decision-maker is risk-averse.
Answer: C
In a time series, “seasonal variation” refers to:
A long-term upward or downward trend in data.
B. Regular fluctuations in data within a specific time period.
C. Random fluctuations without any predictable pattern.
D. Cyclical variations that occur at irregular intervals.
Answer: B
The “Bayes’ theorem” is primarily used for:
Calculating the probability of events based on prior knowledge.
B. Performing hypothesis testing for normal distributions.
C. Estimating population parameters from sample data.
D. Calculating the mean and variance of a sample.
Answer: A
The “variance inflation factor” (VIF) in multiple regression is used to:
Measure the correlation between the dependent and independent variables.
B. Identify if there is multicollinearity among independent variables.
C. Calculate the strength of the regression model.
D. Evaluate the goodness of fit for the regression model.
Answer: B
In the context of linear regression, “heteroscedasticity” refers to:
Constant variance of the residuals across all levels of the independent variable.
B. Non-constant variance of the residuals across different levels of the independent variable.
C. A situation where residuals are uncorrelated with each other.
D. The perfect linear relationship between independent variables.
Answer: B
In a hypothesis test, a “Type II error” occurs when:
A false null hypothesis is not rejected.
B. A true null hypothesis is rejected.
C. A true alternative hypothesis is rejected.
D. A false alternative hypothesis is accepted.
Answer: A
The “Durbin-Watson statistic” is used to detect:
Multicollinearity in a regression model.
B. Heteroscedasticity in a regression model.
C. Autocorrelation of residuals in a regression model.
D. The normality of residuals in a regression model.
Answer: C
In linear programming, the “simplex method” is used to:
Maximize or minimize a linear objective function subject to linear constraints.
B. Solve non-linear optimization problems.
C. Estimate the parameters of a linear regression model.
D. Determine the optimal solution for time series forecasting.
Answer: A
The “Kolmogorov-Smirnov test” is used to:
Compare the means of two independent samples.
B. Test for the normality of data.
C. Test for homogeneity of variances.
D. Compare the observed and expected frequencies of a categorical variable.
Answer: B
“Sampling error” refers to:
The difference between the sample statistic and the population parameter.
B. The bias in the sampling method.
C. The random variation in sample data due to chance.
D. The error introduced by incorrect data collection methods.
Answer: C
“Clustering” in data analysis is used to:
Find a relationship between two variables.
B. Identify groups of similar observations in a dataset.
C. Analyze the distribution of a single variable.
D. Test for causal relationships between variables.
Answer: B
“Monte Carlo simulation” is used to:
Analyze the effect of uncertainty in model predictions.
B. Determine the exact value of a mathematical function.
C. Find the exact solutions to optimization problems.
D. Test hypotheses about data distributions.
Answer: A
In linear regression, the “coefficient of determination” (R²) represents:
The correlation between the dependent and independent variables.
B. The proportion of variance in the dependent variable explained by the independent variables.
C. The significance level of the regression model.
D. The residual error in the regression model.
Answer: B
In the context of optimization, “dual variables” in linear programming represent:
The values of the objective function.
B. The optimal values of the decision variables.
C. The shadow prices or marginal values of constraints.
D. The values of the slack variables.
Answer: C
“Causal inference” refers to:
The process of estimating the effect of an independent variable on a dependent variable.
B. The identification of the most important predictor in a model.
C. The estimation of correlation between two variables.
D. The process of transforming data into a normal distribution.
Answer: A
“Quantile regression” is used to:
Estimate the mean of a dependent variable.
B. Examine the relationship between variables at different quantiles of the dependent variable.
C. Test the normality of residuals in a regression model.
D. Estimate the maximum likelihood for a given data distribution.
Answer: B
In time series analysis, the “autocorrelation function” (ACF) is used to:
Analyze the relationship between past and future values in a time series.
B. Identify the trend in a time series.
C. Test for seasonality in a time series.
D. Measure the randomness of a time series.
Answer: A
In decision analysis, a “payoff table” is used to:
Display the probabilities of different outcomes for a decision alternative.
B. Show the expected value of different decision outcomes.
C. List the possible outcomes and corresponding payoffs for each alternative decision.
D. Calculate the risk of each decision alternative.
Answer: C
The “Gini coefficient” is used to measure:
The level of income inequality in a population.
B. The normality of a dataset.
C. The strength of the linear relationship between two variables.
D. The proportion of variance explained by a regression model.
Answer: A
In multiple regression, “interaction terms” are used to:
Model the relationship between two variables.
B. Estimate the residuals in the model.
C. Examine how the relationship between two variables changes at different levels of a third variable.
D. Calculate the strength of the correlation between two independent variables.
Answer: C
“Theil’s U-statistic” is used to:
Measure the goodness of fit in linear regression models.
B. Test the normality of a dataset.
C. Estimate the inequality in income distributions.
D. Compare the variances of two or more populations.
Answer: C
“Jackknife resampling” is used to:
Estimate the bias and variance of a statistical estimator.
B. Randomly sample observations to create a training dataset.
C. Compute confidence intervals for model parameters.
D. Test hypotheses about population means.
Answer: A
In regression analysis, “model specification errors” refer to:
Including too many predictor variables in the model.
B. Omitting important variables or incorrectly including irrelevant variables.
C. Incorrectly calculating the residuals of the regression model.
D. Not properly normalizing the data before fitting the model.
Answer: B
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