Statistics and Econometrics Questions and Answers

Answer: A

The National Sample Survey, the large scale survey of households by the Government of India, was set up in 1950 on the advice of P. C. Mahalanobis, and its first round was carried out in 1950. So 1950 is the year in which it came into existence. The years 1949, 1951 and 1952 are close dates that are often confused with it. The answer is 1950, option A. The survey is carried out by the National Sample Survey Office, which collects data on households, consumption and employment.

Answer: C

A hypothesis can be stated as a directional statement (predicting the direction of a relation), as a statement of the relation between variables, or as a declarative statement. A general statement is a broad claim and not a testable proposition about variables, so it is not a way of stating a hypothesis. The key gives general statements, option C. A hypothesis is a testable statement and so a general statement is too vague to be tested directly.

Answer: C

A hypothesis is a tentative statement that is formed on the basis of observations of facts and can be tested. It rests on the researcher's observations of the phenomenon, while inferences and conclusions follow after the testing. The answer is observations, option C.

Answer: D

Statistics in the sense of data means numerical facts, that is quantitative data, and raw data, and also descriptive statistics, the summary figures. The tools of analysis belong to statistics as a method (the second meaning of the word) and are not data. The answer is tools of analysis, option D.

Answer: D

Statistics as a method, the tools of analysis, is the statistical method, so collection of data goes with D. The word statistics (the plural) as aggregates of facts goes with C. Analysis of a time series is a case of business statistics, A, and a single datum is not statistics, B. So 1 (D), 2 (C), 3 (A), 4 (B), option D.

Answer: C

The body that is not part of the NSO is the Indian Statistical Institute.

The National Statistics Office under the Ministry of Statistics and Programme Implementation was formed by merging the Central Statistics Office and the National Sample Survey Office, and its divisions include the Data Informatics and Innovation Division, which handles IT and data processing.

The Indian Statistical Institute in Kolkata, founded by P.C. Mahalanobis in 1931, is an autonomous institute of national importance under its own Act of 1959. The ministry funds it, but it is not a constituent of the NSO.

Answer: A

The value is positive for a leptokurtic distribution.

The ratio \(m_{4}/\sigma^{4}\) (often written \(\beta_{2}\)) equals 3 for a normal distribution, so subtracting 3 measures excess kurtosis relative to the normal curve. A leptokurtic distribution is more peaked, with heavier tails, so \(\beta_{2} \gt 3\) and the measure is positive.

A mesokurtic distribution has \(\beta_{2} = 3\), and the normal distribution is the standard mesokurtic case, so both give exactly zero. A platykurtic distribution is flatter than the normal, with \(\beta_{2} \lt 3\), so its value is negative.

Answer: C

The relative measure is the Coefficient of Variation.

It divides the standard deviation by the mean, \(CV = \frac{\sigma}{\bar{x}} \times 100\), so the units cancel and the result is a pure number. That is what makes a measure relative: it can compare the spread of series measured in different units or with very different averages.

Range, mean absolute deviation about the mean and quartile deviation are all absolute measures, expressed in the same units as the data. Each has a relative counterpart (coefficient of range, coefficient of mean deviation, coefficient of quartile deviation), but the options name the absolute forms.

Answer: C

The compound annual growth rate is 16.32%.

The fitted semi-log trend is an exponential growth path:

\[ \begin{aligned} \ln Y_{t} &= 12 + 0.1512\,t \\ Y_{t} &= e^{12}\left(e^{0.1512}\right)^{t} \end{aligned} \]

Each year \(Y\) is multiplied by \(e^{0.1512}\), so the compound rate \(r\) satisfies:

\[ \begin{aligned} 1 + r &= e^{0.1512} \approx 1.1632 \\ r &\approx 0.1632 = 16.32\% \end{aligned} \]

15.12% is the slope itself, which is the instantaneous (continuously compounded) growth rate, not the compound annual rate. 116% treats the growth factor 1.16 as if it were the rate, and 1.16% misplaces the decimal point of that factor.

Answer: A

The model that cannot be estimated is \(Wage_{i} = \alpha + \beta Pass_{i} + \gamma Fail_{i} + u_{1i}\).

Every employee either passes or fails, so \(Pass_{i} + Fail_{i} = 1\) for all \(i\). That sum is exactly the column of ones that carries the intercept \(\alpha\). Including an intercept and both dummies therefore creates perfect multicollinearity, the dummy variable trap: the regressor matrix is not of full rank and least squares cannot separate \(\alpha\), \(\beta\) and \(\gamma\).

The other three are estimable. With both dummies and no intercept, \(\beta\) and \(\gamma\) are simply the mean wages of those who pass and those who fail. With an intercept and one dummy, the omitted category becomes the base group: \(\alpha\) is its mean wage and the dummy's coefficient is the difference between the groups.