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Chapter 6:
Confidence Intervals and Hypothesis Testing
Using Z for the CI and test of the population mean
Learning goals for this chapter:
Understand what inference is and why it is needed.
Know that all inference techniques give us information about the population
parameter.
Explain what a confidence interval is and when it is needed.
Calculate a confidence interval for the population mean when the population
standard deviation is known.
Know the assumptions that must be met for doing inference for the population
mean.
Calculate the needed sample size if you have a predetermined margin of error.
Know how to write hypotheses, calculate a test statistic and Pvalue, and write
conclusions in terms of the story.
Draw Normal curve pictures to match the hypothesis test.
Understand the logic of hypothesis testing and when a hypothesis test is needed.
Use the confidence interval to perform a twosided hypothesis test.
Explain sampling variability and the difference between the population mean and
the sample mean.
Explain the difference between the population standard deviation and the sample
standard deviation.
Know which technique is most appropriate for a story:
confidence interval,
hypothesis test, or simple summary statistics.
When we collect data from our sample, we can calculate sample statistics.
However,
usually we are interested in what is true for the whole population, not just for the sample.
(Remember that a census is very hard and expensive to do well.)
Why can’t we just
accept our sample mean or sample proportion as the official mean or proportion for the
population?
Every time we estimate the statistics
ˆ
,
x p
(sample mean and sample
proportion), we get a different answer due to sampling variability.
Two most common types of formal statistical inference:
Confidence Intervals
:
when we want to estimate a population parameter
Significance Tests
:
when we want to assess the evidence provided by the data in
favor of some claim about the population (yes/no question about the population)
Confidence Intervals
allow us to estimate the population mean or population proportion.
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The true mean or proportion for the population exists and is a fixed number, but we just
don’t know what it is.
Using our sample statistic, we can create a “net” to give us an
estimate of where to expect the population parameter to be.
Confidence interval = net
Population parameter = invisible, stationary butterfly
We don’t know exactly where the butterfly is, but from our sample, we have a pretty
good
estimate of the location.
We don’t need to take a lot of random samples to recreate the sampling distribution with
the population mean μ at its center.
All we need is one Simple Random Sample of size
n.
Because of what we know about the sample mean distribution, we can use that one
sample mean’s confidence interval to infer what the population mean really is.
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 Spring '08
 Staff
 Statistics, Normal Distribution, Statistical hypothesis testing

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