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Unformatted text preview: calculate another
sample mean: e.g., 369.5
3 95± .8
6. 5 8
3 36 ≤µ 3 53
6. 2 ≤ 7. 8 ◦ New interval estimate: ◦ If μ=368, this interval estimate is also true. Interval Estimation can choose a third sample and calculate a third
sample mean: e.g., 360.0
3 00± .8
6. 5 8
3 41 ≤µ 3 58
5. 2 ≤ 6. 8 ◦ New interval estimate: ◦ If μ=368, this interval estimate is not true. Population Mean: σ Known Interval Estimation Recap: suppose that population mean is unknown can choose a sample, calculate a sample mean,
and find an interval estimate for the population
mean in some cases, the interval estimate is true, but not
in all cases
In how many cases will the interval estimate be
true? Population Mean: σ Known Interval Estimation In how many cases will the interval estimate be
true? recall: interval estimate based on finding an interval
symmetrically distributed around the population
mean that includes 95% of the sample means. therefore, 95% of the time, the interval estimate
based on the sample mean will include the
population mean Population Mean: σ Known Interval Estimation In how many cases will the interval estimate be
true? recall: interval estimate based on finding an interval
symmetrically distributed around the population
mean that includes 95% of the sample means. therefore, 95% of the time, the interval estimate
based on the sample mean will include the
population mean
95% confidence that the population mean is in the
interval Population Mean: σ Known
Interval Estimate of a Population Mean: σ Known x ± zα 2 margin
s
za 2 ◦ Interval Estimation ◦ of error
or CONFIDENCE.NORM(alpha,standard_dev,size) size of margin based on level of significance α level
◦ n σ
n of significance represented by α (alpha)
α = Level of Significance = 1 – Confidence confidence
◦
◦ 1 – Level of Signficance
most common are 95%, 90%, and 99% Confidence Levels
Values of zα/2 for most commonly used confidence
lConfidenc
evels:
Confidence
zα/2
e Level
α
α/2...
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 Spring '13

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