CEA Data Analysis & Statistical Methods 3 — Questions and Answers
Question 1: The Central Limit Theorem (CLT) states that as sample size increases, the sampling distribution of the sample mean:
- Approaches the distribution of the population
- Becomes approximately normal regardless of the population distribution (Correct answer)
- Has the same variance as the population
- Converges to a uniform distribution
Correct answer: Becomes approximately normal regardless of the population distribution
The CLT guarantees that the sampling distribution of the mean approaches normality as n increases, even if the underlying population is non-normal.
Question 2: A p-value of 0.03 in a hypothesis test with α = 0.05 means:
- There is a 3% chance the null hypothesis is true
- There is a 3% probability of observing a result this extreme if the null hypothesis is true (Correct answer)
- The effect size is 3%
- 97% of sample means would exceed the observed value
Correct answer: There is a 3% probability of observing a result this extreme if the null hypothesis is true
The p-value is the probability of obtaining a test statistic as extreme as observed, assuming the null hypothesis is true.
Question 3: Which of the following best describes heteroskedasticity in a regression model?
- Residuals are normally distributed
- The variance of the error term is constant across observations
- The variance of the error term changes with the level of an independent variable (Correct answer)
- Independent variables are correlated with each other
Correct answer: The variance of the error term changes with the level of an independent variable
Heteroskedasticity means the spread (variance) of residuals is not constant and often increases or decreases with the magnitude of an explanatory variable.
Question 4: An economist runs a regression and finds the R² = 0.85. This means:
- 85% of the variation in the dependent variable is explained by the independent variables (Correct answer)
- There is an 85% chance the model is correct
- Each coefficient is statistically significant at the 15% level
- The model predicts the dependent variable with 15% error
Correct answer: 85% of the variation in the dependent variable is explained by the independent variables
R² (coefficient of determination) measures the proportion of total variance in the dependent variable that is explained by the regressors.
Question 5: In a box plot, an observation is typically flagged as an outlier if it lies:
- More than 1 standard deviation from the mean
- Beyond 1.5 × IQR from the nearest quartile (Correct answer)
- Below the 5th percentile or above the 95th percentile
- More than 2 standard deviations from the median
Correct answer: Beyond 1.5 × IQR from the nearest quartile
The conventional box plot rule labels values beyond Q1 − 1.5×IQR or Q3 + 1.5×IQR as outliers (shown as individual points).
Question 6: A cointegrated pair of time series is best described as two series that:
- Are both stationary at level
- Share a common long-run stochastic trend (Correct answer)
- Have equal means and variances
- Display identical seasonal patterns
Correct answer: Share a common long-run stochastic trend
Cointegrated series are individually non-stationary (typically I(1)) but a linear combination of them is stationary, reflecting a long-run equilibrium relationship.
Question 7: Stratified random sampling is preferred over simple random sampling when:
- The population is perfectly homogeneous
- Important subgroups must be adequately represented in the sample (Correct answer)
- The sample size is very small
- Sampling cost is the only concern
Correct answer: Important subgroups must be adequately represented in the sample
Stratified sampling divides the population into subgroups (strata) and samples from each, ensuring representation of key segments and often improving precision.
CEA Data Analysis & Statistical Methods 3
The Central Limit Theorem (CLT) states that as sample size increases, the sampling distribution of the sample mean: