PREVIOUS YEAR SOLVED PAPERS - January 2017
- Option : C
- Explanation : Probability Sampling : It is also known as random sampling or chance sampling. Under this design, each item of the universe has equal chance of inclusion in the sample. It is a lottery method in which units are picked up from the whole group by some mechanical process. The results obtained from such a sample can be assured in terms of probability, i.e., we can measure the errors of estimation or the significance of results obtained from a random sample. The is why probability sampling techniques are considered superior to deliberate sampling techniques. Some other sampling techniques under probability sampling are the following:
∎ Simple random sampling
∎ Systematic sampling
∎ Stratified sampling
∎ Cluster sampling
∎ Multistage sampling
∎ Sequential sampling
∎ Multiphase sampling
∎ Double sampling
Non-probability Sampling Procedures : Nonprobability samples are used when the representativeness is not particularly the primary issue. From these samples, one cannot estimate sampling error. Hence, these are also called ‘uncontrolled sampling methods’. This sampling procedure does not afford any basis for estimating the probability that each item in the population has a chance of being included in the example. This type of sampling is also called as deliberate sampling, purposive sampling and judgement sampling. In other words, under non-probability sampling the investigators purposively choose the particular units of the universe for constituting a sample on the basis that the sample will be a typical or representative of the whole. In such a design, personal element has a chance of entering into the selection of the sample.
The investigators may select a sample which shall yield results favourable to their point of view and if this happens, the entire enquiry may get vitiated. There is always the danger of bias entering into this type of sampling technique. But if the investigators are impartial and take sound judgement, the results obtained from the analysis of deliberately selected sample may be reliable. Quota sampling also is a non-probability sampling. Here, the interviewers are simply given quotes to be filled from different strata, with some restriction on how they are to be filled. Actually, the selection of the items for the sample is left to the interviewer’s discretion. This type of sampling is very convenient and relatively inexpensive, but they do not possess the characteristic of random samples. Quota samples are judgement samples and inference drawn are not amenable to statistical treatment in a formal way.
Major forms of non-probability sampling procedures are as follows:
∎ Convenience sampling
∎ Purposive sampling
∎ Quota sampling
| List–I | List–II |
| (a) The ability of test to reject the null hypothesis when it is false. | 1. Level of significance |
| (b) The probability of accepting a false null hypothesis. | 2. Type I error |
| (c) The probability of rejecting a true null hypothesis due to sampling error. | 3. Type II error |
| (d) The probability of rejecting a true null hypothesis. | 4. Power of a test |
Codes
| (a) | (b) | (c) | (d) | |
| 1 | 4 | 2 | 1 | 3 |
| 2 | 4 | 3 | 1 | 2 |
| 3 | 1 | 2 | 3 | 4 |
| 4 | 2 | 3 | 1 | 4 |
18. Which one of the following is a false statement?
- A
The signs of the regression coefficients are always the same.
- B
Correlation coefficient is the geometric mean of the two regression coefficients.
- C
The co-variance between two variables divided by the product of their standard deviations produces the value of coefficient of correlation.
- D
Coefficient of correlation is independent of origin but not of scale.
- Option : B
- Explanation : Properties of Correlation Coefficient
Property-1 : Pearsonian correlation coefficient can not exceed 1 numerically. In other words it lies between –1 and +1.
Symbolically, -1 ≤ r ≤ 1
In other words, r = ± 1 implies perfect positive correlation between the variables and r = –1 implies perfect negative correlation between the variables.
Property-2 : Correlation coefficient is independent of the change of origin and scale.
Property-3 : Two independent variables are uncorrelated but the converse in not true.
- Option : C
- Explanation : Since the coefficient of correlation is the G.M. between the regression coefficients, therefore,
Since r has the same sign as the two regression coefficients so r must be +ve. Hence r = 0.4.
