6-3 Estimating a Population Mean:
σ
Known
In this case, we wish to estimate the population mean,
μ
.
Assumptions
1.
The sample is a simple random sample.
2.
The value of the population standard deviation,
σ
, is known.
3.
Either or both of these conditions are satisfied: The population is normally
distributed or
n
> 30.
The sample mean,
x
, is the best estimate for the population mean,
μ
.
Question: How good is the best estimate?
The confidence interval gives us a range of values instead of a single value. The
difference between the sample mean and the population mean is called the error.
Margin of Error for the Mean:
σ
Known
/ 2
E
z
n
α
σ
=
Confidence Interval Estimate of the Population Mean (with
σ
Known)
/ 2
,
where
x
E
x
E
E
z
n
α
μ
σ
−
<
<
+
=
Example
For the sample of body temperatures from Data Set 4 in the textbook, we have
n
= 106
and
x
=
F. Assume that the sample is a simple random sample and that

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