I make a ppt on Simple Random Sampling (SRS)

1. Simple Random Sampling
Mr. Surajkumar D. Chaudhari
M.Sc. (Statistics), Sem – II, Roll no. : 03
Paper-203 (Sampling Theory)
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2. CONTENTS
• Introduction
• Why Simple Random Sampling?
• Method to get Simple Random Sample
• SRSWR
• SRSWOR
• Pir
(Probability of ith
unit to be selected at rth
draw)
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3. INTRODUCTION
• A Simple Random Sample is a set of individual
units chosen from a large Population.
• In Sample , each individual is chosen randomly
and all individual have same probability to be
selected in the sample at any stage during
Sampling process.
• This process and TECHNIQUE is known as
Simple Random Sampling.
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4. Why Simple Random Sampling?
• The members of the sample are selected
randomly.
• Every member has an equal chance of being
selected in the sample.
• Simple Random Sampling is a suitable
technique for a Population which is highly
homogeneous And having complete
sampling frame And having finite number of
units in the population.
• It is a Simplest way to get Random Sample.
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5. Method to get Simple Random
Sample
• There are two ways to get a Simple Random
Sample:
1. The Lottery Method
2. Random Number Table
• (1) The Lottery Method :
• First we give unique no. to all population units.
Like 1,2,…
• Each number placed in a card of Similar Size,
Similar Shape and Same Colour.
• All cards put in a bowl and mixed well.
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6. • Then Blindfolded person select a one card, and
note down that number written in the selected
card.
• Repeat this process till we reach the desired
Sample Size.
• (2) Random Number Table :
• A Random number table is a series of digits 0 to
9 arranged randomly in rows and columns.
• The table usually contains 5-digit number
arranged in rows and columns.
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7. • Note down number one by one from random
number table, till reach the desired Sample size.
• Using this functions we compute random number
in Excel.
=RAND() and
=RANDBETWEEN(bottom,top) 8

8. SRSWR and SRSWOR
1. Simple Random Sampling With Replacement
(SRSWR) :
• In SRSWR the units selected in the earlier draws are
replaced to the population before the next draws are
made.
• Thus a unit has a chance of being included in the
sample for more than once.
• Number of possible SRSWR sample of size 'n' from
population of size 'N' is, Nn
.
• Probability of realization of a sample ‘s’ from sample
space is
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9. 2. Sample Random Sampling Without Replacement
(SRSWOR) :
• In SRSWOR the units selected in the earlier draws
aren't replaced to the population before the next drawn
are made.
• Thus a unit has only one chance of being included in
the sample.
• Number of possible SRSWOR Sample of size 'n' from
population of size 'N' is,
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10. • Probability of realization of selecting a sample
‘s’ from sample space is
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11. Pir
(Probailiy of ith
unit to be
selected at rth
draw)
• Population size N
• Sample size n
1. Pir
for SRSWR :-
Probability of selecting each sample unit is same
• So,in SRSWR it is easy to show that Probability
of selection ith
unit at rth
draw is
1 2 … r … n-1 n
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12. 2. Pir
for SRSWOR :-
probability of selecting ith
unit at rth
draw
• => Pir
=
• => Pir
=
1 2 … r-1 r
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