Given the following information match the item in List - I with List - II :List - IList - IIa. Rejecting H0, if it is true1. β errorb. Accepting H0, if it is false2. Standard errorc. Probability of rejecting H0, when it is false3. α errord. Measuring sampling variability due to random force4. 1 - β errorCodes :a b c d

The correct code is a-3, b-1, c-4, d-2. Rejecting H0 when it is true is a Type I error, whose probability is α. Accepting H0 when it is false is a Type II error, with probability β. The probability of rejecting H0 when it is false is 1 - β, the power of the test. The variability of a sample statistic arising from random sampling is measured by the standard error. Code D matches all four; code A wrongly pairs power with standard error.

Statistics and Econometrics Questions and Answers

Q: The order condition is

The order condition is a necessary but not sufficient condition for identification.The order condition says that the number of variables excluded from an equation must be at least the number of equations less one. An equation that fails this cannot be identified, so it is necessary. Yet it can be met and the equation still be unidentified, which is why the rank condition is also needed.It is therefore not a sufficient condition, and it is not a condition that is neither necessary nor sufficient.

101.

The order condition is

A.a necessary and sufficient condition for identification.
B.a necessary but not sufficient condition for identification.
C.a sufficient but not necessary condition for identification.
D.a condition that is neither necessary nor sufficient for identification.

Exam Year(s)

UGC NET - 2013,

Answer: B

The order condition is a necessary but not sufficient condition for identification.

The order condition says that the number of variables excluded from an equation must be at least the number of equations less one. An equation that fails this cannot be identified, so it is necessary. Yet it can be met and the equation still be unidentified, which is why the rank condition is also needed.

It is therefore not a sufficient condition, and it is not a condition that is neither necessary nor sufficient.

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102.

Given arithmetic mean = 45, mode = 48, then median =

A.46
B.45
C.48
D.49

Exam Year(s)

UGC NET - 2014,

Answer: A

The median is 46. For a moderately skewed distribution the empirical relation between the three averages is that mode equals three times the median minus twice the mean.

\[ \text{Mode} = 3\,\text{Median} - 2\,\text{Mean} \]

\[ 48 = 3\,\text{Median} - 2(45) \]

\[ \text{Median} = \frac{48 + 90}{3} = 46 \]

The median lies between the mean and the mode, and closer to the mean, so 45, 48 and 49 cannot be right.

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103.

The analysis of variance is carried out by using

A.t-test
B.Z-test
C.\(\chi^{2}\)-test
D.F-test

Exam Year(s)

UGC NET - 2014,

Answer: D

Analysis of variance is carried out using the F-test. ANOVA splits total variation into variation between groups and variation within groups, and the ratio of the two variance estimates follows the F distribution; a large F shows that the group means differ. The t-test and the Z-test compare one or two means, and the \(\chi^{2}\)-test is used for goodness of fit, independence of attributes and a single variance, not for comparing several means through variances.

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104.

Systematic sampling implies that the first item is selected randomly and

A.the other items are selected by lottery method
B.the other items are selected purposively
C.then every \(k^{th}\) item is selected
D.the other items are selected at the will of the investigator

Exam Year(s)

UGC NET - 2014,

Answer: C

In systematic sampling the first item is selected at random and then every k^th item is selected, where k is the sampling interval, the population size divided by the sample size. For instance, with an interval of 10 and a random start at 7, the sample is items 7, 17, 27 and so on. Selecting the rest by lottery is simple random sampling, selecting them purposively or at the investigator's will is judgement sampling, and neither follows a fixed interval.

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105.

Given the following information match the item in List - I with List - II :

List - I	List - II
a. Rejecting H₀, if it is true	1. β error
b. Accepting H₀, if it is false	2. Standard error
c. Probability of rejecting H₀, when it is false	3. α error
d. Measuring sampling variability due to random force	4. 1 - β error

Codes :
a b c d

A.3 1 2 4
B.2 1 4 3
C.2 4 1 3
D.3 1 4 2

Exam Year(s)

UGC NET - 2014,

Answer: D

The correct code is a-3, b-1, c-4, d-2. Rejecting H₀ when it is true is a Type I error, whose probability is α. Accepting H₀ when it is false is a Type II error, with probability β. The probability of rejecting H₀ when it is false is 1 - β, the power of the test. The variability of a sample statistic arising from random sampling is measured by the standard error. Code D matches all four; code A wrongly pairs power with standard error.

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106.

Assertion (A) : Geometric mean is theoretically considered as the best average to construct index numbers.

Reason (R) : Geometric mean is used if the range of observations is extremely large.
Codes :

A.Both (A) and (R) are true and (R) is the correct explanation of (A).
B.Both (A) and (R) are true, but (R) is not the correct explanation of (A).
C.(A) is true, but (R) is false.
D.(A) is false, but (R) is true.

Exam Year(s)

UGC NET - 2014,

Answer: A

Both Assertion (A) and Reason (R) are true, and (R) is the correct explanation of (A). The geometric mean is regarded as the best average for index numbers because it averages ratios properly: it gives equal weight to equal relative changes and satisfies the time reversal test. When the observations cover a very wide range, the geometric mean is preferred because it is much less affected by extreme values than the arithmetic mean. Price relatives commonly vary widely, which is why this property makes the geometric mean the theoretically best average for constructing index numbers.

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107.

The estimated regression equation of a firm producing scooter tyres is : \(\ln y = -3.56 + 0.31 \ln X_1 - 0.05 \ln X_2 + 0.53 \ln X_3 + 0.37 \ln X_4\), \(\bar{R}^{2} = 0.89\) (Y = output and \(X_1\) to \(X_4\) are factor inputs). Assuming that all the estimated parameters are statistically significant from zero, the firm has

A.constant returns to scale
B.decreasing returns to scale
C.increasing returns to scale
D.neutral returns to scale

Exam Year(s)

UGC NET - 2014,

Answer: C

The firm has increasing returns to scale. In a log-linear (Cobb-Douglas) form the coefficients are the output elasticities of the inputs, and returns to scale are given by their sum:

\[0.31 - 0.05 + 0.53 + 0.37 = 1.16\]

A sum above 1 means that raising all inputs by a given proportion raises output by a larger proportion. A sum of 1 would be constant returns and below 1 decreasing returns, and 'neutral returns' is not a term for returns to scale.

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108.

The test statistic used to test the significance of the adjusted coefficient of multiple determination ( \(\bar{R}^{2}\) ) is :

A.t-test
B.Z-test
C.\(\chi^{2}\)-test
D.F-test

Exam Year(s)

UGC NET - 2014,

Answer: D

The significance of the adjusted coefficient of multiple determination is tested with the F-test, which tests whether all slope coefficients are jointly zero, equivalent to testing that the \(R^{2}\) is not different from zero.

The t-test and Z-test examine a single coefficient. The chi-square test is used for variance or goodness-of-fit questions, not for the joint significance of a regression.

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109.

The technique used to estimate the over-identified system of simultaneous equations is

A.ordinary least squares
B.maximum likelihood
C.limited information maximum likelihood
D.two stage least squares

Exam Year(s)

UGC NET - 2014,

Answer: D

An over-identified system of simultaneous equations is estimated by two stage least squares, which uses all the excluded instruments to give a consistent estimate.

Ordinary least squares is biased and inconsistent here because of the correlation between the regressors and the errors. Maximum likelihood is a general method and limited information maximum likelihood is a different single-equation method, but the key accepts two stage least squares as the technique asked for.

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110.

The sources of auto correlation among the following are :

I. Omitted explanatory variables
II. Interpolation in the statistical observation
III. Mis-specification of the true random term 'ν'
IV. Economic variables to move together over time
Codes :

A.I and II only
B.I, II and III only
C.I, III and IV only
D.All of the above

Exam Year(s)

UGC NET - 2014,

Answer: B

The sources of autocorrelation are omitted explanatory variables, interpolation in the statistical observations and mis-specification of the true random term (I, II and III).

Economic variables that move together over time (IV) give rise to multicollinearity among regressors, not serial correlation of the errors. Options that include IV are therefore wrong.

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