CPT Section D Quantitative Aptitude Chapter 15. Prof. Bharat Koshti

Transcription

1 CPT Section D Quantitative Aptitude Chapter 15 Prof. Bharat Koshti

2 Different Methods of Sampling 1. Probability Sampling Methods 2. Non-Probabilistic Sampling Methods 3. Mixed Sampling Methods

3 (1) Probability Sampling Methods In this method there is a fixed/ pre-assigned Probability for each member to be selected in the sample from the population. (a) Simple Random Sampling(SRS): In this method there is an equal chance/probability for every member being selected in the sample.

4 There are two methods in Simple Random Sampling- One Simple Random Sampling With replacement (SRSWR)& another is Simple Random Sampling without replacement(srswor). Simple Random sampling is useful when- (i) The population size is not very large. (ii) The population under study is not heterogeneous.

5 A government income tax auditor wants to choose a sample of 5 out of 11 IT returns to audit Generate Person Das Random # Tripathi Joshi Agarwal Shah Purohit Singhal Bhandari Kulkarni Arora Gupta Sorted Person 1 Bhandari Random # Joshi Purohit Shah Arora Singhal Kulkarni Agarwal Gupta Das Tripathi

6 (b) Stratified Random Sampling: This method is very suitable for large & heterogeneous population. Here the population is divided into a number of strata or sub-populations or groups. These groups are made in such a way that They are homogeneous among themselves They are heterogeneous between themselves

7 Samples are drawn from these strata by SRS(Simple Random Sampling) method. Then all these samples are added together to form the desired stratified sample. Thus n=n 1 +n 2 +n 3 +.+n k Where n 1, n 2, n 3,.. n k are the samples from 1 st stratum, 2 nd stratum,3 rd stratum,.. k th stratum etc.

8 After the population has been stratified, we can use simple random sampling to generate the complete sample Population Sample Size Income Category Proportion n = 400 n =1000 Below Rs. 30,000 25% Rs. 30,000- Rs. 49,999 40% Rs. 50,000- Rs. 69,999 20% Above Rs. 70,000 15% Here sample sizes are proportional to population sizes and hence it is called as Proportional Allocation or Bowely s Allocation.

9 Note that when the strata variances do not differ significantly among themselves then we use Proportional Allocation or Bowely s Allocation. Here we consider n i α N i where i = 1,2,3 k When the strata variances differ significantly among themselves then we use Neyman s Allocation. Here n i α N i S i where i = 1,2,3 k

10 (c) Multistage Sampling: Under this method sampling is done in several stages. e.g. In order to find the extent of unemployment in India we may take samples from state, district, police station and household as the first stage, second stage, third stage & ultimate sampling units respectively.

11 (2) Non-Probability Sampling: This type of sampling solely depend on the discretion of the investigator or sampler. Judgement or Purposive Sampling : In this method the sampler applies his belief, prejudice, experience to select the sample. This type of sampling is purely subjective & estimates obtained from it varies from person to person. Note that no statistical hypothesis can be tested on the basis of this sampling.

12 (3) Mixed Sampling: It is a mixture or combination of probability and non probability sampling i.e. some part of sampling is done by probability sampling and other is done by non probability sampling. e.g. Systematic Sampling.

13 Here sampling procedure is as follows- 1.In this sampling Population is divided into certain no. (say n ) of strata or groups. 2.Each group is having equal number of members say k. 3.Then first select from the first group one member randomly i.e. from 1 to k any one is selected randomly. 4.Then from the remaining groups we select the member having same location number. e.g. If we select 3 rd member from the first group then from the 2 nd group we select also 3 rd member, like that from all the remaining groups. Here every group must have equal no. of members.

14 (a) Block or cluster sampling (b) Area sampling (c) Quota sampling (d) Deliberate, purposive or judgment sampling. Answer: D

15 (a) A probabilistic sampling (b) A non- probabilistic sampling (c) A mixed sampling (d) Both (b) and (c). Answer: A

16 (a) Sample size is proportional to the population size (b) Sample size is proportional to the sample SD (c) Sample size is proportional to the sample variance (d) Population size is proportional to the sample variance. Answer: A

17 (a) Simple random sampling (b) Multistage sampling (c) Stratified sampling (d) Systematic sampling Answer: B

18 (a) Simple random sampling (b) Stratified sampling (c) Multistage sampling (d) Systematic sampling Answer: D

19 (a) true (b) false (c) both (d) None Answer: A

20 (a) True (b) false (c) both (d) none Answer: A

21 (a) strata (b) strati (c) start (d) None Answer: A

22 (a) multi- stage (b) Stratified (c) Random (d) None Answer: C

23 (a) multi-stage (b) Random (c) purposive (d) None Answer: B

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