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Constructing a Confidence
Interval about
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(%20(Section%209.1%20topic).doc_files/image004.gif){kind=small}
known)
A
simple random sample of size n is drawn from a population that is normally
distributed with population standard deviation,
,
known to be 13. The sample mean
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,
is found to be 108. (c) (103.96, 112.04); decreases
(a) Compute the 96% confidence interval if the sample size, n, is 25. (102.66, 113.34)
(b) Compute the 96% confidence interval if the sample size, n, is 10. How does decreasing the sample size affect the margin of error, E? (99.56, 116.44); increases
(c) Compute the 88% confidence interval if the sample size, n, is 25. Compare the results to those obtained in part (a). How does decreasing the level of confidence affect the size of the margin of error, E?
(d) Could we have computed the confidence intervals in part (a)-(c) if the population had not been normally distributed? Why? No
(e) Suppose an analysis of the sample data revealed three outliers greater than the mean. How would this affect the confidence interval?
(a.) A
random sample of size n=25 is selected from a population that is normally
distributed with a standard deviation,
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,
equal to 13. The sample mean,
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,
is equal to 108.
To
estimate%20(Section%209.1%20topic).doc_files/image014.gif){kind=small}
,
the population mean, using a 96% confidence interval, press
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STAT, highlight TESTS and select 7:Zinterval.
On the
first line of the display, you can select Data or Stats. For this example,
select Stats because you have the sample mean but not the actual data. Press
ENTER. Move to the next line and enter 13, the value of
.
On the next line, enter 108, the value for
,
the sample mean. On the next line, enter the sample size, 25. For C-Level,
enter .96 for a 96% confidence interval. Move the cursor to Calculate.
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Press ENTER.
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