Tag: UGC NET Economics – Unit 3: Statistics and Econometrics

UGC NET Economics Unit 3-Statistics and Econometrics-MCQs

Section A: Probability & Distributions

1. The probability of an impossible event is:
A) 0 B) 1 C) 0.5 D) ∞
✅ Answer: A
📘 Explanation: An impossible event cannot occur, so its probability = 0.

2. The sum of probabilities of all exhaustive events equals:
A) 0 B) 1 C) 100 D) Depends on events
✅ Answer: B
📘 Because all possible outcomes together make probability 1.

3. If A and B are independent, $P (A \cap B)$ =
A) $P (A) + P (B)$ B) $P (A ∣ B)$ C) $P (A) P (B)$ D) 0
✅ Answer: C
📘 For independent events, joint probability is product of individual probabilities.

4. The expected value of a constant is:
A) 0 B) The constant itself C) 1 D) Undefined
✅ Answer: B
📘 Expected value (mean) of a constant is the constant itself.

5. In a normal distribution, the mean, median, and mode are:
A) Different B) Equal C) Opposite D) Undefined
✅ Answer: B
📘 The normal curve is symmetric, so all three are equal.

6. The Poisson distribution is used for:
A) Continuous data B) Rare discrete events C) Large samples D) Normal data
✅ Answer: B
📘 Poisson models rare events (like accidents per hour).

7. The sum of probabilities in a binomial distribution equals:
A) 0 B) n C) 1 D) Mean
✅ Answer: C
📘 The total of all probabilities always sums to 1.

8. In a normal distribution, about 95% observations lie within:
A) ±1σ B) ±2σ C) ±3σ D) ±4σ
✅ Answer: B
📘 According to the empirical rule, 95% of data lies within 2 standard deviations.

9. If mean = 50 and variance = 25, then standard deviation =
A) 5 B) 25 C) 2 D) 10
✅ Answer: A
📘 $S D = \sqrt{V a r i a n c e} = \sqrt{25} = 5.$

10. Central Limit Theorem implies that:
A) Population distribution becomes normal
B) Sample mean becomes normal for large n
C) Sample variance = population variance
D) Mean = 0
✅ Answer: B
📘 CLT → sampling distribution of mean → normal as n increases.

Section B: Descriptive Statistics

11. Mean of 5, 10, 15 is:
A) 10 B) 15 C) 12 D) 30
✅ Answer: A
📘 $(5 + 10 + 15) / 3 = 10.$

12. Median of {1, 3, 3, 6, 7, 8, 9} =
A) 3 B) 6 C) 7 D) 5
✅ Answer: B
📘 Middle term = 6.

13. The most frequent value in a dataset is called:
A) Mean B) Median C) Mode D) Range
✅ Answer: C
📘 Mode = most occurring value.

14. Range =
A) Mean – median B) Max – Min C) SD² D) Mode + mean
✅ Answer: B
📘 Range measures total spread of data.

15. The coefficient of variation (CV) =
A) $\frac{M e a n}{S D} \times 100$ B) $\frac{S D}{M e a n} \times 100$ C) $S D + M e a n$ D) $S D - M e a n$
✅ Answer: B
📘 CV measures relative dispersion.

16. If r = +1, then correlation is:
A) Perfect positive B) Perfect negative C) No correlation D) Moderate
✅ Answer: A
📘 +1 → perfect positive linear relationship.

17. Karl Pearson’s r is used to measure:
A) Association B) Central tendency C) Variability D) Forecasting
✅ Answer: A
📘 It measures linear association between two variables.

18. Fisher’s Ideal Index =
A) Laspeyres × Paasche B) $\sqrt{L \times P}$ C) L/P D) L + P
✅ Answer: B
📘 Geometric mean of Laspeyres and Paasche indices.

19. If the correlation coefficient is 0, the regression slope will be:
A) 0 B) 1 C) Undefined D) Infinite
✅ Answer: A
📘 Zero correlation → no linear relationship → slope = 0.

20. If data are highly spread out, the SD will be:
A) Low B) High C) Zero D) Negative
✅ Answer: B
📘 Greater dispersion → higher SD.

Section C: Sampling & Inference

21. Sampling error arises due to:
A) Mistakes in data B) Incomplete sampling C) Using sample instead of population D) Wrong hypothesis
✅ Answer: C
📘 Occurs because sample may not perfectly represent population.

22. In random sampling, every item has:
A) Equal chance B) Unequal chance C) No chance D) Weightage-based chance
✅ Answer: A
📘 Random → equal probability for all.

23. Stratified sampling is used when:
A) Population is homogeneous B) Population is heterogeneous C) Sample is large D) Randomness is not possible
✅ Answer: B
📘 Used to ensure all subgroups (strata) are represented.

24. Sampling distribution refers to:
A) Population distribution B) Distribution of a statistic over samples C) Normal curve D) Regression model
✅ Answer: B
📘 Sampling distribution = distribution of sample statistics like mean.

25. Standard Error =
A) $\frac{σ}{\sqrt{n}}$ B) $\frac{n}{σ}$ C) $σ^{2}$ D) $n σ$
✅ Answer: A
📘 SE shows variability of sample mean.

26. Type I error =
A) Rejecting true H₀ B) Accepting false H₀ C) Accepting true H₀ D) Rejecting false H₀
✅ Answer: A
📘 α-error: reject a true null hypothesis.

27. Type II error =
A) Reject true H₀ B) Accept false H₀ C) Increase sample size D) Wrong distribution
✅ Answer: B
📘 β-error: fail to reject a false null hypothesis.

28. When population variance is unknown and n < 30, use:
A) z-test B) t-test C) F-test D) χ²-test
✅ Answer: B
📘 t-test handles small samples.

29. The χ² test is used for:
A) Comparing means B) Testing independence C) Regression D) Correlation
✅ Answer: B
📘 Chi-square → tests association or goodness of fit.

30. Power of a test =
A) 1 − α B) 1 − β C) α + β D) α × β
✅ Answer: B
📘 Power = probability of correctly rejecting false H₀.

Section D: Regression & Econometrics

31. Regression equation: $Y = a + b X + u$ — here “b” is:
A) Constant B) Slope coefficient C) Error D) Mean
✅ Answer: B
📘 b measures rate of change of Y per unit X.

32. In simple linear regression, number of parameters =
A) 1 B) 2 C) 3 D) Depends on variables
✅ Answer: B
📘 a (intercept) and b (slope).

33. BLUE stands for:
A) Best Linear Unbiased Estimator B) Basic Least Unbiased Equation C) Biased Linear Ultimate Estimation D) None
✅ Answer: A
📘 Gauss-Markov theorem: OLS estimators are BLUE.

34. OLS estimators are BLUE when:
A) Errors are correlated B) Homoscedasticity holds C) Mean of errors ≠ 0 D) Multicollinearity exists
✅ Answer: B
📘 Constant error variance (homoscedasticity) is one key assumption.

35. Multicollinearity refers to:
A) Correlation among independent variables B) Correlation between errors C) Correlation between X and u D) Serial correlation
✅ Answer: A
📘 Independent variables highly correlated → multicollinearity.

36. Heteroscedasticity means:
A) Constant variance B) Changing variance of errors C) Equal variance D) No variance
✅ Answer: B
📘 Non-constant variance → violates OLS assumption.

37. Autocorrelation occurs when:
A) Errors are independent B) Errors depend on past errors C) Variance constant D) Errors are random
✅ Answer: B
📘 Common in time series data.

38. The problem of simultaneous equations arises because:
A) Variables are exogenous B) Variables are interdependent C) Errors are normal D) Sample is small
✅ Answer: B
📘 Endogenous variables appear on both sides → simultaneity.

39. Recursive models:
A) Have feedback loops B) Have one-way causation C) Are non-identifiable D) Require IV estimation
✅ Answer: B
📘 Recursive → unidirectional, solvable by OLS.

40. Identification problem arises in:
A) Single equation B) Simultaneous equations C) Cross-section data D) Random sampling
✅ Answer: B
📘 Occurs when equations cannot be uniquely estimated.

41. Logit and Probit models are used when dependent variable is:
A) Continuous B) Binary C) Time series D) Multivariate
✅ Answer: B
📘 Discrete choice → 0/1 outcome.

42. Instrumental variables are used to correct:
A) Heteroscedasticity B) Endogeneity C) Autocorrelation D) Multicollinearity
✅ Answer: B
📘 IVs eliminate endogeneity bias.

43. Two-Stage Least Squares (2SLS) is used for:
A) Recursive models B) Non-recursive models C) OLS D) Binary models
✅ Answer: B
📘 2SLS → estimation of simultaneous equations.

Section E: Time Series & Miscellaneous

44. Components of time series include all except:
A) Trend B) Seasonal C) Cyclical D) Random Sampling
✅ Answer: D
📘 Random sampling isn’t a time series component.

45. The long-term movement in a time series is called:
A) Trend B) Seasonal variation C) Cycle D) Random
✅ Answer: A
📘 Trend shows overall direction.

46. Seasonal variations repeat:
A) Monthly B) Annually C) Daily D) Randomly
✅ Answer: B
📘 Seasonal → same pattern every year.

47. Stationary time series has:
A) Changing mean B) Constant mean and variance C) Random trend D) Increasing variance
✅ Answer: B
📘 Stationarity → constant mean, variance, covariance.

48. ARIMA models are used for:
A) Regression B) Forecasting time series C) Sampling D) Testing hypotheses
✅ Answer: B
📘 ARIMA = AutoRegressive Integrated Moving Average → forecasting.

49. Autocorrelation refers to:
A) Correlation between different variables B) Correlation between current and past values C) Randomness D) Error-free data
✅ Answer: B
📘 Measures serial dependence in time series.

50. Durbin-Watson test is used to detect:
A) Heteroscedasticity B) Multicollinearity C) Autocorrelation D) Nonlinearity
✅ Answer: C
📘 DW statistic → tests autocorrelation in regression residuals.

November 3, 2025

UGC NET Economics Unit 3 -Statistics and Econometrics

1. Probability Theory

Concept of Probability:

Probability measures the likelihood of an event occurring.
It always lies between 0 and 1.

$P (A) = \frac{Number of favourable outcomes}{Total number of outcomes}$

0 → Impossible event
1 → Certain event

Types of Probability:

Classical – based on equally likely outcomes (e.g., coin toss).
Empirical – based on past data (e.g., rainfall probability).
Subjective – based on personal judgment.

🔹 Important Concepts:

Independent Events: Occurrence of one doesn’t affect another.
Mutually Exclusive Events: Cannot occur simultaneously.
Conditional Probability:

$P (A ∣ B) = \frac{P (A \cap B)}{P (B)}$
Bayes’ Theorem: Used for revision of probabilities based on new information.

2. Probability Distributions

Discrete Distributions:

Binomial Distribution:

$P (x) = (\binom{n}{x}) p^{x} q^{n - x}$

Used for success-failure experiments.
Poisson Distribution:
Used when events are rare and independent (e.g., accidents).

$P (x) = \frac{e^{- λ} λ^{x}}{x!}$

🔹 Continuous Distribution:

Normal Distribution:
Bell-shaped curve; symmetric around mean.
Mean = Median = Mode.
Used in sampling, hypothesis testing, etc.

3. Moments and Central Limit Theorem

🔹 Moments:

Moments describe shape of a distribution.

1st moment → Mean
2nd moment → Variance
3rd moment → Skewness (asymmetry)
4th moment → Kurtosis (peakedness)

🔹 Central Limit Theorem (CLT):

As sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of population distribution.

💡 This theorem justifies the use of normal probability in statistics.

4. Descriptive Statistics

🔹 Measures of Central Tendency:

Mean (Average):

$\overset{ˉ}{X} = \frac{\sum X_{i}}{n}$
Median: Middle value when data arranged in order.
Mode: Most frequent value.

🔹 Measures of Dispersion:

Indicate how data values are spread around the mean.

Range
Variance
Standard Deviation
Coefficient of Variation (CV)

🔹 Correlation:

Shows relationship between two variables.
Karl Pearson’s coefficient:

$r = \frac{\sum (X - \overset{ˉ}{X}) (Y - \overset{ˉ}{Y})}{\sqrt{\sum (X - \overset{ˉ}{X})^{2} \sum (Y - \overset{ˉ}{Y})^{2}}}$

Values of r lie between -1 and +1.

🔹 Index Numbers:

Measure changes in price, quantity, or value over time.
Types:

Price Index (e.g., CPI, WPI)
Quantity Index
Value Index

Formulas:

Laspeyres Index: Base year weights
Paasche Index: Current year weights
Fisher’s Index: Geometric mean of the two (Ideal index)

5. Sampling Methods & Sampling Distribution

🔹 Sampling Methods:

Random Sampling – every unit has equal chance.
- Simple Random
- Stratified Random
- Systematic Sampling
- Cluster Sampling
Non-random Sampling – convenience or judgment-based.

🔹 Sampling Distribution:

Distribution of a statistic (like mean) from repeated random samples.
Used to estimate population parameters.

Standard Error (SE) = Standard deviation of a sampling distribution.

6. Statistical Inference and Hypothesis Testing

🔹 Estimation:

Point Estimate: single value (e.g., sample mean).
Interval Estimate: range of values (confidence interval).

🔹 Hypothesis Testing Steps:

State Null (H₀) and Alternative (H₁) hypotheses
Choose significance level (α)
Select appropriate test statistic (Z, t, χ², F)
Define rejection region
Calculate test statistic
Accept or reject H₀

🔹 Common Tests:

Z-test: Large samples (n > 30)
t-test: Small samples
χ²-test: Goodness of fit or independence
F-test: Compare two variances

7. Linear Regression Models

🔹 Simple Linear Regression:

$Y = α + β X + u$

where

Y = Dependent variable
X = Independent variable
u = Random error term

🔹 Properties of OLS (BLUE):

OLS estimators are Best Linear Unbiased Estimators when:

Linear in parameters
Expected value of error = 0
Homoscedasticity (constant variance)
No autocorrelation
No perfect multicollinearity
Errors are normally distributed

8. Identification Problem

Occurs in simultaneous equation systems when parameters cannot be uniquely estimated.

Identification Types:

Under-identified: Insufficient restrictions → No unique solution
Exactly identified: Just enough restrictions → Unique solution
Over-identified: More restrictions than needed → Multiple estimates

9. Simultaneous Equation Models

🔹 Recursive Models:

Equations arranged in sequence
No feedback
Can be solved by OLS

🔹 Non-Recursive Models:

Feedback present (mutual dependence)
Require Two-Stage Least Squares (2SLS) or Instrumental Variables (IV) for estimation.

10. Discrete Choice Models

Used when dependent variable is categorical (0/1, yes/no).

Types:

Logit Model – uses logistic function
Probit Model – uses cumulative normal distribution

Example: Probability of employment, adoption of technology, etc.

11. Time Series Analysis

Components of Time Series:

Trend (T): Long-term direction.
Seasonal (S): Regular pattern within a year.
Cyclical (C): Long-term up and down movements (business cycles).
Irregular (I): Random variations.

Models:

Additive Model: $Y = T + S + C + I$
Multiplicative Model: $Y = T \times S \times C \times I$

Stationarity:

A series is stationary when mean, variance, and covariance remain constant over time.

Autocorrelation:

Measures correlation between current and past values of a series.

AR, MA, ARMA, ARIMA Models:

Used for forecasting and economic time series modeling.

🧾 Quick Summary Table

Topic	Key Concept / Formula	Use / Importance
Probability	$P (A) = \frac{f}{n}$	Foundation of statistics
Normal Distribution	Bell-shaped curve	Basis for inference
CLT	Sample mean → normal	Enables hypothesis testing
Correlation	$r \in [- 1, + 1]$	Strength of relationship
Regression	$Y = a + b X$	Predictive analysis
BLUE	Best Linear Unbiased Estimator	Gauss-Markov theorem
Hypothesis Testing	Z, t, χ², F tests	Decision making
Identification	Unique estimation issue	Econometric modeling
Logit/Probit	Binary dependent variable	Discrete choice
Time Series	Trend, Seasonality, Cyclic	Forecasting

November 3, 2025