Section 1.2

Random Samples

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Sampling techniques

• Simple Random Sampling

• Stratified Sampling• Systematic Sampling• Cluster Sampling• Convenience

Sampling

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• Simple Random Sample of n measurements from a population is a subset of the population selected in a manner such that

• Every sample of size n from the population has an equal chance of being selected.

• Every item in the population has an equal chance of being included.

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Not random sampling:

Ask for volunteers to respond to a survey.Choose the next five customers entering a store.

Random sampling:• Draw names “from a hat.”• Use a random number table to select a

sample.• Use a random number generator.

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Number all members of the population Sequentially Use a table, calculator or computer to select random numbers from the numbers assigned to population members.Create the sample using population members with numbers corresponding to selected numbers.

How to draw a random sample:

Simulation

• Provide mathematical imitations of “real” phenomena.

• May use a random number table to simulate a process.

• (Good in nuclear reactors, cloud formation, cardiology etc.)

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Example of SimulationUse the random-number table to simulate the outcomes

of tossing a balanced (that is, fair) quarter 10 times.(a) Possible outcomes: 2, heads or tails(b) Assign an even digit or heads and odd digit for tails.

Then starting at block 3 of row 2 of table 1 in the appendix, list the 10 single digits 7 1 5 4 9 4 4 8 4 3(c) The outcomes associated with the

10 digits T T T H T H H H H T(d) If you start with different block and row will you get

the same sequence of outcomes? It is possible, but not very likely

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Sampling TechniquesSampling with Replacement• When a number is selected for a sample, it is not removed

from the population.Stratified Sampling• Population is divided into groups.• Random samples are drawn from each group.Systematic Sampling• Population is arranged in sequential order.• Select a random starting point.• Select every “kth” item.Cluster Sampling• Population is divided into sections.• Some sections are randomly selected.• Every item in selected sections is included in sample. 1.2 / 7

Sampling TechniquesConvenience Sampling• Use whatever data is readily available.• Risk severe bias.

Summary of Sampling techniques• Random Sampling• Stratified Sampling• Systematic Sampling• Cluster Sampling• Convenience Sampling

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Which sampling technique is described?

College students are waiting in line for registration. Every eighth person in line is

surveyed.

Systematic sampling

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Convenience sampling

Which sampling technique is described?

College students are waiting in line for registration. Students are asked to volunteer to respond to a survey.

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Stratified sampling

Which sampling technique is described?

In a large high school, students from every homeroom are randomly selected to

participate in a survey

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Simple random sampling

Which sampling technique is described?

An accountant uses a random number generator to select ten accounts for audit.

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To determine students’ opinions of a new registration method, a college randomly selects five majors. All

students in the selected majors are surveyed.

Cluster sampling

Which sampling technique is described?

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