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Match List - I with List - II

List - I (Statistic) List - II (Standard Error)
A. Sample Mean (x̅) I. \(\sqrt{\left(\sigma_{1}^{2}/2 n_{1}\right)+\left(\sigma_{2}^{2}/2 n_{2}\right)}\)
B. Sample Variance (s2) II. \(\sqrt{\left(\sigma_{1}^{2}/n_{1}\right)+\left(\sigma_{2}^{2}/n_{2}\right)}\)
C. Difference of two independent sample means (x̅1 − x̅2) III. \(\sigma/\sqrt{n}\)
D. Difference of two independent sample standard Deviations (s1 − s2) IV. \(\sigma^{2} \sqrt{\frac{2}{n}}\)

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UGC NET Paper 2: Economics 30th Sept 2020
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  1. A - III, B - IV, C - II, D - I
  2. A - III, B - II, C - IV, D - I
  3. A - III, B - IV, C - I, D - II
  4. A - I, B - III, C - II, D - IV

Answer (Detailed Solution Below)

Option 1 : A - III, B - IV, C - II, D - I
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Important Points

Statistic Standard error
Sample mean
  • The standard error of the sample mean is shown as
  • \(\sigma/\sqrt{n}\)
Sample variance
  • The standard error of sample variance is shown as
  • \(\sigma^{2} \sqrt{\frac{2}{n}}\)
Difference of two independent sample means
  • The standard error of the difference between two independent sample means is shown as:
  • \(\sqrt{\left(\sigma_{1}^{2}/n_{1}\right)+\left(\sigma_{2}^{2}/n_{2}\right)}\)
Difference of two independent sample standard deviations
  • The difference of two independent sample standard deviations is shown as
  • \(\sqrt{\left(\sigma_{1}^{2}/2 n_{1}\right)+\left(\sigma_{2}^{2}/2 n_{2}\right)}\)

 Additional Information Standard error: The standard deviation of a sampling distribution of a statistic is known as standard error, and it is denoted by SE.

  • The standard error is used to express the accuracy or precision of the estimate of population parameter because the reciprocal of SE is the measure of reliability or precision of statistic.
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