Confidence Intervals: Continued
In general:
•
Bigger Confidence > Bigger Interval
•
Bigger Sample Size > Smaller Interval
•
If you want to have a lot of confidence, but not a huge interval, increase the sample size.
Examples:
For each of the following stories, identify the type of problem (mean or proportion), check the
necessary assumptions, construct the confidence interval, and interpret the results.
1.
A survey asks 231 college students how many sexual partners they have had in their lives.
The
sample mean was 4.641 and the sample standard deviation equals 6.33.
a)
Is the parameter being estimated the population proportion or the population mean?
b)
Are the assumptions for a confidence interval for the population parameter met?
c)
Construct a 95% CI for the parameter.
d)
Interpret the interval.
2.
In 2004, the GSS asked participants about their opinions about spanking.
They asked the
following questions, “Do you strongly agree, agree, disagree, or strongly disagree that it is
sometimes necessary to discipline a child with a good, hard spanking?” 35 out of 892 respondents
said that they agreed or strongly agreed that it was sometimes necessary.
a)
Is the parameter being estimated the population proportion or the population mean?
b)
Are the assumptions for a confidence interval for the population parameter met?
c)
Construct a 99% CI for the parameter.
d)
Interpret the interval.
3.
As part of a class study, sixteen students were randomly selected from the University of Florida
student phone book and asked if they prefer bagels or doughnuts.
Ten out of the sixteen students
surveyed said they prefer bagels.
a)
Is the parameter being estimated the population proportion or the population mean?
b)
Are the assumptions for a confidence interval for the population parameters met?
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Construct a 95% CI for the parameter.
7.4 How Do We Choose the Sample Size for the Study?
When planning a study, we can determine how large the sample needs to be to estimate the parameter
within a given margin or error, with the desired confidence.
Determining Sample Size for Estimating a Population Proportion
Margin of error for a CI for p is: m =
ˆ
ˆ
(1
)
p
p
z
n

When we don’t know p we use p = 0.5.
Solving for n:
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 Fall '07
 Ruffin
 Statistics, Null hypothesis, Statistical hypothesis testing

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