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Transcript
Inferential statistics are generally used to make
inferences about the population based on the
measurements taken from the sample.
Two applications:
1. Estimation
2. Test of Hypothesis
point estimate - a single
value/number that can be
regarded as a sensible value
for the population parameter.
Interval estimate- an interval of
possible values of an unknown
population parameter
 Ex.
Parameter
μ
σ2
Estimator
s2
 Confidence
Interval
◦ A confidence interval gives an
estimated range of values which
is likely to include an unknown
population
parameter,
the
estimated range being calculated
from a given set of sample data.
Confidence Interval for the Mean μ
Case 1. Large sample size n and known
variance σ2
Def. If
is used to estimate an
unknown mean μ with large sample
size n and known variance, then we can
be (1- α)100% confident the mean will
be within
1. Compute a 95% confidence interval for
μ when σ= 3.0, = 58.3, and n= 100.
2. Suppose observation on the speed of
50 vehicles yield a sample mean of 65
mph. Assume the standard deviation of
vehicle speed is known equal to 6 mph.
Determine the 2-sided 99% confidence
intervals of the mean speed.
Def. If
is used to estimate an
unknown mean μ with small sample
size n and unknown variance, then we
can be (1- α)100% confident the mean
will be within
Example.
1. Compute a 95% confidence interval for
μ when s= 3.0, = 55.3, and n= 16.
2. Concrete placed on a structure was
cored and the following results were
obtained:
3566, 3779, 3887, 3912, 4005
4142, 3405, 3402, 4039, 3372 psi
Determine the 95% 2-sided confidence
interval of the mean concrete strength.
Example
1. How large a sample is needed if we want to
be 95% confident that actual average speed
of all vehicles will not exceed by 1.5mph?
2. How large a sample is needed if we want to
be 98% confident so that true proportion of
household subscribed to PLDT will be within
2%?
