Download S-300 C-7 Formula Notes.cwk

Chapter 7 Formulas
Estimating a Population Proportion p
from a sample of size n with a Confidence Level of 1− α
If the population is known to be normal or nˆp ≥ 5 and nqˆ ≥ 5 then:
€
the Confidence Interval for the population proportion
P
with a Confidence Level of 1− α is found by
€
€
pˆ qˆ
ˆp − E < p < ˆp + E where E = zα 2
n
€
€
Estimating A Population
Mean µ
€
from a sample of size n with a Confidence Level of 1− α
with σ known.
€ size n is greater than 30 then:
If the population is known to be normal or the sample
€
€
The Confidence Interval for the population mean µ is given by
σ
x − E < µ < x + E where E = zα 2
n
€
€
€
Estimating A Population Mean µ
from a sample of size n with a Confidence Level of 1− α
when σ is NOT known.
€
If the population is known to be normal or the sample size n€is greater than 30 then:
The Confidence €
Interval for the population mean µ is given by
s
x − E < µ < x + E where E = tα 2 x
n
€
€ Estimating A Population Standard deviation σ
€
from a sample of size n with a Confidence Level of 1− α
If the population is normal then:
€
The Confidence Interval for the Population Standard deviation
σ is given by
€
(n − 1)(sx ) 2
(n − 1)(sx )2
<
σ
<
χ 2R
χ L2
€
Chapter 7 Notes
Statistics 300
€
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Determining the Sample Size for Estimating the Population Proportion
To determine the sample size n that will provide an estimate of the population proportion with a
confidence level of 1− α and and error of no greater than a given percentage E use the following
equation and round the answer up to the next higher whole number.
2 .25
n = zα 2 • 2
€
E
( )
Note: The Population Proportion is a percent expressed as a decimal and the margin of error will
also be a percent expressed as a decimal.
€
Determining the Sample Size for Estimating the Population Mean
To determine the sample size n that will provide an estimate of the population mean with an error no
greater than a given margin of error E with a confidence level of 1− α use the following equation and
then round the answer up to the next higher whole number.
 zα 2 • σ 2
n =
 if σ€ IS known
 E 
Note: The Population Mean is a real number (not a percent) and the margin of error will also be a real
€
number.
€
Determining the Sample Size for Estimating the Population Standard Deviation
To determine the sample size n that will provide an estimate of the population standard deviation σ
with a confidence level of 1− α and with an error of no greater than a given percentage use the
following tables.
Sample size n to estimate σ
Sample size n to estimate €
σ
€
To be 95 %
of the value of σ
To be 99 %
of the value of σ
confident that the the sample size n
confident that the the sample size n
€
€
estimate is within should be at least
estimate is within should be at least
€
€
1%
19, 204
1%
33,218
5%
767
5%
1,335
10 %
191
10 %
335
20 %
47
20 %
84
30 %
20
30 %
37
40 %
11
40 %
21
50 %
7
50 %
13
Chapter 7 Notes
Statistics 300
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