Math 2311
Class Notes for Section 7.4
7.4  Confidence Interval for a Population Mean
Recall that formula for a confidence interval is
statistic
±
margin of error
.
When we are making an
inference about a population mean, the statistic will be our sample mean,
x
.
The critical value we use to find the margin of error for our calculation will be based on whether the
population or sample standard deviation is known.
When the population standard deviation is known,
we use the formula
x
±
z
*
σ
n
and when it is unknown, we will need to find the sample standard
deviation,
s
, and use the formula
x
±
t
*
s
n
where
t
* is the
t
critical value based on
n
– 1 degrees of
freedom.
So, what is
t*
?
t
distribution vs. standard normal distribution:
How do we find critical values for a
t
distribution?
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The assumptions for a population mean are:
1.
The sample must be an SRS from the population of interest.
2.
The data must come from a normally distributed population.
If this is not the case or if we are
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 Spring '08
 HAFEEZ
 Normal Distribution, Standard Deviation

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