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Sampling
Probability sampling: it is the one in which each sample has the same probability of being chosen.
Purposive sampling: it is the one in which the person who is selecting the sample is who tries to make the sample representative, depending on his opinion or purpose, thus being the representation subjective.
No-rule sampling: we take a sample without any rule, being the sample representative if the population is homogeneous and we have no selection bias.
There are different types of probability sampling:
• Random sampling with and without replacement.
• Systematic sampling.
• Stratified sampling.
• Cluster sampling.
• Other types of sampling techniques
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Numerical on Sampling
A jar contains 3 red marbles, 7 green marbles and 10 white marbles. If a marble is drawn at random, what is the probability that marble drawn is white?
Solution :
Here Red = 3
Green = 7
White = 10
Hence total sample space is (3+7+10)= 20
Out of 20 one ball is drawn n(S) = {c(20,a.} = 20
To find the probability of occurrence of one White marble out of 10 white ball
n(R)={c(10,a.} = 10
Hence P(R) = n(R)/n(S)
= 10/20 = 1/2
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A sack contains 4 black balls 5 red balls. What is probability to draw 1 black ball and 2 red balls in one draw?
Solution :
Out of 9, 3 (1 black & 2 red) are expected to be drawn)
Hence sample space
n(S) = 9c3
= 9!/(6!×3!)
= 362880/4320
= 84
Now out of 4 black ball 1 is expected to be drawn hence
n(B) = 4c1
= 4
Same way out of 5 red balls 2 are expected be drawn hence
n(R) = 5c2
= 5!/(3!×2!)
= 120/12
= 10
Then P(B U R) = n(B)×n(R)/n(S)
i.e 4×10/84 = 10/21
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Time Series:
- 4 Types of variation in Time series:
- Secular Trend – Over a long period of time - Consumer price Index
- Cyclical Fluctuation – Business cycle
- Seasonal variation – Doctor – Seasons (changes within a year)
- Irregular variation – Unpredictable, Earth Quake, war etc.
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Estimation refers to the process by which one makes inferences about a population, based on information obtained from a sample.
Point Estimate vs. Interval Estimate
Statisticians use sample statistics to estimate population parameters. For example, sample means are used to estimate population means; sample proportions, to estimate population proportions.
An estimate of a population parameter may be expressed in two ways:
- Point estimate. A point estimate of a population parameter is a single value of a statistic. For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P.
- Interval estimate. An interval estimate is defined by two numbers, between which a population parameter is said to lie. For example, a < x < b is an interval estimate of the population mean μ. It indicates that the population mean is greater than a but less than b.
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