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Posted after class
WEEK 11 – Mon, Nov 8
Lower Estimates  (1 – α)100% Confidence Level
OneSided Confidence Intervals
Guidelines from the Centers for Medicare & Medicaid Services state “In most
situations, the lower limit of a onesided 90 percent confidence interval should be used
as the amount of overpayment to be demanded for recovery from the physician or
supplier.”
CI for µ  Case σ is known
Book (N indefinitely large)
N specified – Correct Formula
Discuss limitations.
CI for µ  Case σ is unknown
Book (N indefinitely large)
N specified – Correct Formula
Use
with n – 1
df
(degrees of freedom).
If you use the ttable in
the book and the
df
value is not in the table, go to the row above
the
missing value.
Discuss limitations.
CI for p (appropriate for large n)
Book (N indefinitely large)
N specified – Correct Formula
Discuss limitations.
Example of Lower Estimate
.
The xcharacteristic of a population of size 900 has
unknown mean and unknown standard deviation.
A 90% lower estimate is needed for the
population mean.
A simple random sample of 48 units is selected.
The sample has
average 36.54 and standard deviation 22.45.
Calculate the lower estimate.
Ans.
32.34
1
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OneSided Confidence Intervals
CI for µ  Case σ is known
Book (N indefinitely large)
N specified – Correct Formula
Discuss limitations.
CI for µ  Case σ is unknown
Book (N indefinitely large)
N specified – Correct Formula
Use
with n – 1
df
(degrees of freedom).
If you use the ttable in
the book and the
df
value is not in the table, go to the row above
the
missing value.
Discuss limitations.
CI for p (appropriate for large n)
Book (N indefinitely large)
N specified – Correct Formula
Discuss limitations.
Example
.
The 600 parts in a bin has an unknown proportion p of parts that will not pass
inspection.
A simple random sample of 150 parts from the bin is inspected and it is found
that 12 of the 150 will not pass inspection.
A 95% upper estimate is needed for the
number of parts in the bin that will not pass inspection.
Calculate the upper estimate.
Ans.
The upper estimate for p is 0.1116 which multiplied by 600 gives the answer 66 or
67 parts.
2
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This note was uploaded on 12/11/2010 for the course STT 315 taught by Professor Anderson during the Spring '08 term at Michigan State University.
 Spring '08
 Anderson

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