own and the population is normal. This is Student t distributed with v = n – 1 degrees of freedom.
x = xin
s2= i2x(xi)2nn1
FinOp 250
Chapter 12
Book Notes
INFERENCE ABOUT A POPULATION MEAN WHEN THE
STANDARD DEVIATION IS UNKNOWN
The confidence interval estimator and the test statistic were derived from the sampling
distribution of the sample mean with
known, expressed as
σ
=
z

/
x
μσ n
Now, we take the approach that if the population mean in unknown, so is the population
standard deviation. We substitute the sample standard deviation “s” in the place of the
unknown population standard deviation ”
”.
σ
Test Statistic for μ when
is unknown:
σ
=
t

/
x μs n
Confidence Interval Estimator of μ when
is unknown:
σ
±
/
= 
x
tα 2 sn
v
n 1
Checking the required conditions
The mathematical process that derived the Student t distribution is robust, which means
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 Spring '08
 KOUZEHKANANI
 Statistics, Normal Distribution, confidence interval estimator

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