Chapter 7.1 statistics
•
The
degrees of freedom
for this t statistic come from the sample standard deviation
s
in
the denominator of t
•
The density curves of the t(k) distributions are smaller in shape to the standard normal
curve.
•
That is, they are symmetric about 0 and are bellshaped
•
The spread of the t distribution is a bit greater than that of the standard normal
distribution
•
This is due to the extra variability caused by substituting the random variable s for the
fixed parameter σ
•
T distributions has more probability in the tails and less in the center that does the
standard normal distribution
•
The one sample
t
confidence interval
o
Suppose that an SRS of size n is drawn from a population having unknown mean µ. A
level C confidence interval for µ is:
X(bar) ± MOE
o
In this formula, the margin of error is: MOE= t*SE= t*(s/
)
where t* is the value for the
t(n1) density curve with area C betweent* and t*.
o
This interval is exact when the population distribution is normal and is approximately
correct for large n in other cases
•
The onesample t test
o
Suppose that an SRS of size n is drawn from a population having unknown mean µ.
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 Spring '09
 Gemberling
 Normal Distribution, Standard Deviation, standard normal distribution, population distribution

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