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:
Matching Statistical Concepts: LIST-I and LIST-II
This section provides a detailed explanation to correctly match the terms listed in LIST-I with their corresponding definitions in LIST-II. Understanding these fundamental statistical concepts is essential for accurate data analysis and interpretation.
Overview of LIST-I and LIST-II Items
Here are the items presented in both lists:
| 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 |
Detailed Explanation of Matches
A. Sampling error Analysis
Sampling error is the variation that happens between a statistic calculated from a sample and the corresponding parameter in the population. This difference arises purely due to the random chance involved in selecting the sample, meaning it's a natural consequence of not surveying the entire population. It represents the expected difference between sample statistics and population parameters.
- Correct Match: III. Variation among sample statistics due to change
B. Parameters Analysis
Parameters are numerical values that summarize data for an entire population. They describe characteristics of the whole group being studied, unlike statistics which describe characteristics of a sample. For example, the average age of all students in a university is a parameter.
- Correct Match: I. Values that describe the characteristics of a population
C. Sampling fraction Analysis
The sampling fraction quantifies the size of the sample relative to the size of the population. It is calculated as the ratio of the sample size to the population size. For instance, if a sample of 100 people is taken from a population of 1000, the sampling fraction is 100/1000.
- Correct Match: IV. Proportion of the population contained in a sample
D. Standard error Analysis
The standard error measures the precision of a sample statistic as an estimate of a population parameter. Specifically, it is the standard deviation of the sampling distribution of that statistic. It indicates how much sample statistics are likely to vary if repeated samples were drawn from the same population.
- Correct Match: II. The standard deviation of the sampling distribution
Conclusion: The Correct Match
Synthesizing the explanations above, the correct pairings are:
A-III, B-I, C-IV, D-II
This set of matches accurately defines each statistical term presented.
Important Questions from Statistics
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:
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 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
