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# Types of samples: Independent, dependent, and matched pairs

1. Determine whether the sampling method is independent or dependent for the following example. A researcher wants to know whether the newly issued "state" quarters have a mean weight that is different from "traditional" quarters. He randomly selects 18 "state" quarters and 16 "traditional" quarters. Their weights are compared.

2. Determine whether the sampling method is independent or dependent for the following example. A researcher wants to know whether the price of a one night stay at a Holiday Inn Express Hotel is less than the price of a one night stay at a Red Roof Inn Hotel. She randomly selects 8 towns where the location of the hotels is close to each other and determines the price of a one night stay.

3. Dependent samples are often referred to as matched pairs samples. For example, we have decided to lose weight in a Watch Watchers class so all of us weigh in at the beginning of class and follow a prescribed diet. Then we weigh in at the end of class and the means score are compared before and after the diet. Hopefully, we have lost some weight. The scores should show a significant difference. Provide another example of a matched pairs sample.

#### Solution Preview

The difference between independent and dependent samples comes down to whether you would expect some correlation (or similarity) between items in each sample. If you have dependent samples, knowing something (for example, a score) about Sample A may help you predict something about Sample B. If you have independent samples, knowing a score in Sample A shouldn't help you predict a score in Sample B.

Let's look at this in terms of the examples you've asked about.

1. We have a situation where we have quarters that have been produced by different states (NEW) and quarters that have been produced by the federal mint (OLD). Our researcher randomly samples quarters from each source (NEW and OLD). Now, you may be thinking that we know something about how much quarters weigh from the Old source and so that makes these dependent samples, since knowing something about the Old sample tells us ...

#### Solution Summary

Explains whether the sampling method provides independent or dependent samples for two examples. Describes an example of a matched pairs sample.

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