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means would be between 362.12 and 373.88 grams. σ Known Example
Find an interval symmetrically distributed around the population
mean that includes 95% of the sample means.
Sampling distribution: µ= 6; σ = for n = 25
38 x 3
x find zscores for 2.5% and 97.5%: z = ±1.96 2.5% find corresponding sample means:
−
z = xσ µ x
x
lower tail :
upper tail : Interval Estimation −1.96 = x −µ
3
−5.88 = x − µ 1.96 = x −µ
3
5.88 = x − µ sampling error—difference between
sample mean and population mean xL 95% xU 1.96 μ 1.96 2.5% σ Known Example
Find an interval symmetrically distributed around the population
mean that includes 95% of the sample means.
Sampling distribution: µ= 6; σ = for n = 25
38 x 3
x find zscores for 2.5% and 97.5%: z = ±1.96 2.5% find corresponding sample means:
x ± 5.88
−
z = xσ µ x
x
lower tail :
upper tail : Interval Estimation −1.96 = x −µ
3
−5.88 = x − µ If sample mean
is known, use to
find a range for
the population
mean: x ± 5.88 1.96 = x −µ
3
5.88 = x − µ sampling error—difference between
sample mean and population mean xL 95% xU 1.96 μ 1.96 2.5% σ Known Example
Find an interval symmetrically distributed around the population
mean that includes 95% of the sample means.
Sampling distribution: µ= 6; σ = for n = 25
38 x 3
x find zscores for 2.5% and 97.5%: z = ±1.96 2.5% find corresponding sample means:
−
z = xσ µ x
x
lower tail :
upper tail : Interval Estimation −1.96 = x −µ
3
−5.88 = x − µ If sample mean
is known, use to
find a range for
the population
mean: x ± 5.88 xL 95% xU 2.5% 1.96 μ 1.96 1.96 = x −µ
3
5.88 = x − µ sampling error—difference between
sample mean and population mean 5.88 is the
margin of
error σ Known Example
Find an interval symmetrically distributed around the population
mean that includes 95% of the sample means.
Sampling distribution: µ= 6; σ = for n = 25
38 x 3
x find zscores for 2.5% and 97.5%: z = ±1.96 find corresponding sample means:
−
z = xσ µ x
x
lower tail :
upper tail : Interval Estimation −1.96 = x −µ
3
−5.88 = x...
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This document was uploaded on 03/05/2014.
 Spring '13

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