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Confidence Intervals with a Single Sample Using Either Z or T Distribution
I. An international dormitory wants to see how long, on average, its members have been in the
United States.
Out of 105 people in the dorm, 18 were sampled and averaged 4.5 years in
country with a standard deviation of 2.12 years.
Construct a 90 percent confidence interval
estimate for the dorms member’s average time in the United States.
1)
Find out whether to use Z or t critical;
2)
In example above, we use t critical since number sampled is less than 30.
3) Write formula.
+/– (t critical) ( s/√n).
It is given that n=18 and the confidence level is 90%.
T critical equals 17 ,
(n–1 degrees of freedom)
and an alpha of .10 (1.00–.90).
Reading across for alpha and twotailed (ie. level of significance) and reading down for dfs, our
t critical =
1.740 (ie. 17 dfs, alpha=.10)
Solution:
=4.5; t critical = 1.740; s=2.12;
n=18
4.5 + –
1.740 (2.12/√18)
4.5 + – 1.740(.50)
4.5 + – .869=
(3.631, 5.37)
Interpretation: 90% confident that true population mean is between (3.631
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This note was uploaded on 09/08/2010 for the course SOCS 15 at San Jose State University .
 '10
 Cohn,SaulUri

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