copyright © 2014 pearson education. all rights reserved. 1.2-1 1.2 sampling learning goal...

Copyright © 2014 Pearson Education. All rights reserved. 1.2-1

1.2 Sampling

LEARNING GOALUnderstand the importance of choosing a representative sample and become familiar with several common methods of sampling.

Copyright © 2014 Pearson Education. All rights reserved. 1.2-2Slide 1.2- 2

DefinitionA _____________is the collection of data from every member of a population.

DefinitionA _________________is a sample in which the relevant characteristics of the sample members are generally the same as the characteristics of the population.


EXAMPLE 1 A Representative Sample for Heights

Suppose you want to determine the mean height of all students at your school. Which is more likely to be a representative sample for this study: the men’s basketball team or the students in your statistics class?


Bias

DefinitionA statistical study suffers from ____________if its design or conduct tends to favor certain results.


EXAMPLE 2 Why Use Nielsen?

Nielsen Media Research earns money by charging television stations and networks for its services. For example, NBC pays Nielsen to provide ratings for its television shows. Why doesn’t NBC simply do its own ratings, instead of paying a company like Nielsen to do them?


Sampling Methods

•Simple Random Samples

A _______________is one in which every member of the population has an equal chance of being selected to be part of the sample.

With __________________every possible sample of a particular size has an equal chance of being selected.


EXAMPLE 3 Telephone Book Sampling

You want to conduct an opinion poll in which the population as all the residents in a town. Could you choose a simple random sample by selecting names from the local telephone book?


Sampling Methods


•Systematic Sampling

A type of sampling in which we use a system such as choosing every 50th member of a population.


EXAMPLE 5 When Systematic Sampling FailsYou are conducting a survey of students in a co-ed dormitory in which males are assigned to odd-numbered rooms and females are assigned to even-numbered rooms. Can you obtain a representative sample when you choose every 10th room?


Sampling Methods



•Convenience Samples

The sample is chosen for convenience rather than by a more sophisticated procedure.


EXAMPLE 6 Salsa Taste TestA supermarket wants to decide whether to carry a new brand of salsa, so it offers free tastes at a stand in the store and asks people what they think. What type of sampling is being used? Is the sample likely to be representative of the population of all shoppers?


Sampling Methods•Simple Random Samples



•Cluster SamplesCluster sampling involves the selection of all members in randomly selected groups, or clusters.


EXAMPLE 7 Gasoline Prices

You want to know the mean price of gasoline at gas stations located within a mile of rental car locations at airports. Explain who you might use cluster sampling in this case.


Sampling Methods•Simple Random Samples



•Cluster Samples

•Stratified Samples

Stratified sampling involves randomly selecting members from each stratum.


EXAMPLE 8 Unemployment Data

The U.S. Labor Department surveys 60,000 households each month to copile its unemployment reprot. To select these households, the Department first groups cities and counties into about 2000 geographic areas. It then ramdomly selects households to survey within these geographic areas.

How is this an example of stratified sampling?

What are the strata?

Why is stratified sampling important in this case?


Summary of Sampling Methods

Keep in mind the following three key ideas:• A study can be successful only if the sample is

representative of the population.

• A biased sample is unlikely to be a representative sample.

• Even a well-chosen sample may still turn out to be unrepresentative just because of bad luck in the actual drawing of the sample.


Simple Random Sampling: We choose a sample of items in such a way that every sample of the same size has an equal chance of being selected.

Every sample of the same size has an equal chance of being selected. Computers are often used to generate random numbers.


Systematic Sampling: We use a simple system to choose the sample, such as selecting every 10th or every 50th member of the population.

Select every kth member.


Convenience Sampling: We use a sample that happens to be convenient to select.

Use results that are readily available.


Cluster Sampling: We first divide the population into groups, or clusters, and select some of these clusters at random. We then obtain the sample by choosing all the members within each of the selected clusters.

Divide the population into clusters, randomly select some of those clusters, then choose all members of the selected clusters.


Stratified Sampling: We use this method when we are concerned about differences among subgroups, or strata, within a population. We first identify the strata and then draw a random sample within each stratum. The total sample consists of all the samples from the individual strata.

Partition the population into at least two strata, then draw a sample from each.

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