Sampling Methods: Caiib Paper 1 (Module B), Unit 2
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So, here we are providing “Unit 2: Sampling Methods” of “Module B: Business Mathematics” from “Paper 1: Advanced Bank Management (ABM)”.
The Article is Caiib Unit 2: Sampling Methods
- Sampling is a process used in statistical analysis in which a predetermined number of observations are taken from a larger population. The methodology used to sample from a larger population depends on the type of analysis being performed.
Types of sampling
There are two methods of selecting from populations
- Non- random or judgement sampling
- Random or probability sampling
- A probability sampling method is any method of sampling that utilizes some form of random selection. In order to have a random selection method, you must set up some process or procedure that assures that the different units in your population have equal probabilities of being chosen.
Type of Random Sampling
There are four main type of random sampling
- Simple Random Sampling (SRS)
- Stratified Sampling
- Cluster Sampling
- Systematic Sampling
- Simple Random Sampling (SRS): Simple Random Sampling selects samples by methods that allow each possible sample to have an equal probability of being picked and each item in the entire population to have an equal chance or being included in the sample.
- Systematic Sampling: In systematic sampling, elements are selected from the population at a uniform level that is measured in time, order, or space. If we wanted to interview every twentieth student on a college campus, we would choose a random starting point in the first twenty names in the student directory and then pick every twentieth name thereafter.
- Stratified Sampling: To use stratified sampling, we divide the population into relatively homogenous groups, called strata. Then we use one of two approaches. Either we select at random from each stratum a specified number of elements corresponding to the proportion of that stratum in the population as a whole or we draw an equal number of elements from each stratum and give weight to the results according to the stratum’s proportion of total population.
- Cluster Sampling: In cluster sampling, we divide the population into groups or clusters and then select a random sample of these clusters. We assume that these individual clusters are representative of the population as a whole. If a market Research team is attempting to determine by sampling the average number of television sets per household in a large city, they could use a city map and divide the territory into blocks and then choose a certain number of blocks (clusters) for interviewing. Every household in each of these blocks would be interviewed. A well designed cluster sampling procedure can produce a more precise sample at considerably less cost than that of simple random sampling.
- A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population.
- Standard deviation of the distribution of the sample means is called the standard error of the mean.
Numerical on Sampling
Q1. A sack contains 3 pink balls and 7 green balls. What is probability to draw one pink ball and two green balls in one draw?
Q2.A sack contains 4 black balls 5 red balls. What is probability to draw 1 black ball and 2 red balls in one draw?
Out of 9, 3 (1 black & 2 red) are expected to be drawn)
Hence sample space
n(S) = 9c3
Now out of 4 black ball 1 is expected to be drawn hence
n(B) = 4c1
Same way out of 5 red balls 2 are expected be drawn hence
n(R) = 5c2
Then P(B U R) = n(B)×n(R)/n(S)
i.e 4×10/84 = 10/21
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