Chapter 7
Sampling
By Boundless
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In statistics, a population includes all members of a defined group that we are studying for data driven decisions.
![Thumbnail](../../../../../figures.boundless-cdn.com/17955/square/sample.jpg)
A sample is a set of data collected and/or selected from a population by a defined procedure.
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A random sample, also called a probability sample, is taken when each individual has an equal probability of being chosen for the sample.
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Random assignment helps eliminate the differences between the experimental group and the control group.
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Surveys and experiments are both statistical techniques used to gather data, but they are used in different types of studies.
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Incorrect polling techniques used during the 1936 presidential election led to the demise of the popular magazine, The Literary Digest.
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In the 1948 presidential election, the use of quota sampling led the polls to inaccurately predict that Dewey would defeat Truman.
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When conducting a survey, a sample can be chosen by chance or by more methodical methods.
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Even when using probability sampling methods, bias can still occur.
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The Gallup Poll is a public opinion poll that conducts surveys in 140 countries around the world.
Telephone surveys can reach a wide range of people very quickly and very inexpensively.
Chance error and bias are two different forms of error associated with sampling.
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The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size.
Knowledge of the sampling distribution can be very useful in making inferences about the overall population.
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Learn to create a sampling distribution from a discrete set of data.
![Thumbnail](../../../../../figures.boundless-cdn.com/18027/raw/boxplot-vs-pdf.jpg)
When we have a truly continuous distribution, it is not only impractical but actually impossible to enumerate all possible outcomes.
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The mean of the distribution of differences between sample means is equal to the difference between population means.
![Thumbnail](../../../../../figures.boundless-cdn.com/18062/raw/standard-deviation-diagram.jpg)
The overall shape of a sampling distribution is expected to be symmetric and approximately normal.
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The central limit theorem for sample means states that as larger samples are drawn, the sample means form their own normal distribution.
![Thumbnail](../../../../../figures.boundless-cdn.com/18040/raw/standard-deviation-diagram.jpg)
Expected value and standard error can provide useful information about the data recorded in an experiment.
![Thumbnail](../../../../../figures.boundless-cdn.com/18059/raw/standard-deviation-diagram.jpg)
The normal curve is used to find the probability that a value falls within a certain standard deviation away from the mean.
The expected value is a weighted average of all possible values in a data set.
![Thumbnail](../../../../../figures.boundless-cdn.com/17994/square/voter-poll.jpeg)
The Gallup Poll is an opinion poll that uses probability samples to try to accurately represent the attitudes and beliefs of a population.
![Thumbnail](../../../../../figures.boundless-cdn.com/18086/raw/us-unemployment-measures.jpg)
Labor force surveys are the most preferred method of measuring unemployment due to their comprehensive results and categories such as race and gender.
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Gregor Mendel's work on genetics acted as a proof that application of statistics to inheritance could be highly useful.
- Describing Variability