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Paired t-test example for statistics students

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Community policing strategies have been useful in some jurisdictions to reduce crime. As Police Captain, you wish to run an experiment to see whether it will work in your city. In each of 10 neighborhoods you record the number of arrests for violent offenses for 90 days prior to implementing a community policing strategy and for 90 days after the program has been running for 6 months.

Neighborhood Before After
1 55 42
2 62 59
3 57 58
4 69 60
5 65 58
6 88 81
7 76 70
8 55 51
9 54 56
10 65 63
646 598

Did community policing work? What are the null and alternative hypotheses? What is your conclusion [use alpha of 1%]?

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Solution Preview

For this question you will need to do a paired t test as both data sets come from the same neighborhood, or the "before and after" type of experiment design.

The following formula will be used:

t observed = dbar - md/ sdbar

Where dbar is the average of all difference values between sets, md is equal to 0 (because of paired data), and sdbar is equal to sd/square root n.

The null hypothesis in this case is that there will not be a difference in mean violent crime offenses before and after implementing a community policing strategy.

Ho: mean before = mean after.

The alternative hypothesis is that there will be a difference between mean violent crime offenses before and after the policing strategry is implemented.

Ha: ...

Solution Summary

A complete worked through solution for a paired t-test statistics problem.