Alicia Deal
093004
CJ 685
Assignment #5
1.) What is the purpose of confidence intervals?
The confidence interval is the range of values or an interval within which the population
value falls.
It is an estimated interval that we are reasonably confident contains the true
population value “over the long run.”
The advantage is that by stipulating a range of
values instead of a point estimate, the population parameter is more likely to be included.
2.) Describe the differences between the z distribution and the t distribution.
When is it
appropriate to use the z distribution for estimation?
The central limit theorem only applies to largesized samples, thus the z distribution is
used.
Therefore, if our sample is small, we must utilize statistics that violate this large
sample assumption.
When our research dictates that we have no choice and must utilize a
small sample, the t distribution is typically used to make inferences from the sample
mean, X, the population mean, mu (
).
At small sample sizes, the t distribution is flatter
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 Fall '08
 STAFF
 Statistics, Normal Distribution

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