Match List - I with List - II.
List - I List - II A. Sample proportion P = x/n I. $\frac{\sigma}{\sqrt{n}}$ B. Sample variance $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(xi-x̄)^2$ II. $\sigma^2 \sqrt{\frac{2}{n}}$ C. Sample variance $S^2 = \frac{1}{n} \sum_{i=1}^{n}(xi-x̄)^2$ III. $\sigma^2 \sqrt{\frac{2}{(n-1)}}$ D. Sample mean $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}xi$ IV. $\sqrt{\frac{\pi(1-\pi)}{n}}$
Choose the correct answer from the options given below :
The question requires matching items from List-I (statistical concepts) with their corresponding formulas or standard errors from List-II.
Statistical Formula Matching
A. Sample Proportion Match
List-I item A is the sample proportion, defined as $P = \frac{x}{n}$. The standard error of the sample proportion is given by $\sqrt{\frac{\pi(1-\pi)}{n}}$, where $\pi$ is the population proportion. This matches List-II item IV.
Match: A - IV
B. Unbiased Sample Variance Match
List-I item B is the unbiased sample variance, $S_1^2 = \frac{1}{n-1} \sum_{i=1}^{n}(x_i-\bar{x})^2$. The approximate standard error for the unbiased sample variance is $\sigma^2 \sqrt{\frac{2}{n-1}}$. This matches List-II item III.
Match: B - III
C. Biased Sample Variance Match
List-I item C is the biased sample variance, $S^2 = \frac{1}{n} \sum_{i=1}^{n}(x_i-\bar{x})^2$. The approximate standard error for the biased sample variance is $\sigma^2 \sqrt{\frac{2}{n}}$. This matches List-II item II.
Match: C - II
D. Sample Mean Match
List-I item D is the sample mean, $\bar{x} = \frac{1}{n} \sum_{i=1}^{n}x_i$. The standard error of the sample mean is $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation. This matches List-II item I.
Match: D - I
Final Matching Summary
Combining the individual matches, we get:
- A matches with IV ($\sqrt{\frac{\pi(1-\pi)}{n}}$)
- B matches with III ($\sigma^2 \sqrt{\frac{2}{(n-1)}}$)
- C matches with II ($\sigma^2 \sqrt{\frac{2}{n}}$)
- D matches with I ($\frac{\sigma}{\sqrt{n}}$)
This corresponds to the combination A-IV, B-III, C-II, D-I.
Important Questions from Statistics
- Match the LIST-I with LIST-II
LIST-I LIST-II A. Sampling error I. Values that describe the characteristics of a population B. Parameters II. The standard deviation of the sampling distribution C. Sampling fraction III. Variation among sample statistics due to change D. Standard error IV. Proportion of the population contained in a sample
Choose the correct answer from the options given below: Given below are two statements one is labelled as Assertion (A) and the other is labelled as
Reason (R).
Assertion (A): Additive model considers the total of various components resulting in the given
values of the over all time series and it is stated as:
$Y=T+C+S+I$
Reason (R): Multiplicative model assumes that the various components interact in a
multiplicative manner to produce the given values of the over all time series and
can be stated as $Y=T \times C \times S \times I$
In the light of the above statements, choose the most appropriate answer from the options given
below:
- The measurement or determinations of length, height, weight, volume, area, pressure etc. comes under:
- Which of the following options explain what a 'mean' assumes ?
(i) an interval level of measurement
(ii) a nominal level of measurement
(iii) an ordinal level of measurement
(iv) a ratio level of measurement - Match List I with List II:
List I List II (a) Alpha Level (I) The index of magnitude or strength of relationship (b) Level of Significance (II) The point at which one would reject the null hypothesis and accept the alternate hypothesis (c) Critical Region (III) Another name for alpha level (d) Effect size indicatior (IV) A marked area which would be called a rare event
