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Unformatted text preview: he same. A. G. Baker, Department of Statistics
G.
University of South Carolina; Slide 49
University
49 Interval Width, Level of Confidence
Interval
and Sample Size
and
At a given sample size, as level of
confidence increases, interval width
__________.
__________.
At a given level of confidence as sample
size increases, interval width __________.
size
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 50
University
50 Calculate Sample Size Before
Calculate
Sampling!
Sampling!
The width of the interval is determined by:
The
± zα / 2 σ
n Suppose we wish to estimate the mean to a
maximum error of e: Max error = e = zα / 2 σ
n zα / 2σ n= e 2 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 51
University
51 Plastic Injection Molding
A plastic injection molding process for a
part that has a critical width dimension
historically follows a normal distribution
with a standard deviation of 8.
with
What sample size is required to estimate
the true mean width to within + 2 units at
units
95% confidence?
95%
What sample size is required to estimate
the true mean width to within + 2 units at
units
99% confidence?
99%
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 52
University
52 If we don’t have prior knowledge of the
have
standard deviation, but can assume we
are sampling from a normal
population…
population
Instead of using a zvalue to calculate the
Instead
value
confidence interval…
confidence
P (−tα / 2 Y −µ
<
< +tα / 2 ) = (1 − α )
s/ n P( µ = Y ± tα / 2 s
) = (1 − α )
n G. Baker, Department of Statistics
G.
University of South Carolina; Slide 53
University
53 Interval Estimate of the Mean
Standard Normal t 1α α/2 4 3 df=n1 tα/2 2 1 0 α/2 1 +tα/2 2 3 4 (1 – α) 100% Confidence Interval
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 54
University
54 Plastic Injection Molding –
Plastic
Reworded
A plastic injection molding process for a
part that has a critical width dimension
historically follows a normal distribution.
historically
A recent sample of four yielded a sample
mean of 101.4 and sample standard
deviation of 8.
deviation
Estimate the true mean width with a 95%
confidence interval.
confidence
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 55
University
55 Hypothesis Testing G. Baker, Department of Statistics
G.
University of South Carolina Combustion Engine
The nominal power produced by a student
The
designed combustion engine is assumed to be at
least 100 hp. We wish to test the alternative
that the power is less than 100 hp.
that
Let µ = nominal power of engine.
Let
QQ plots shows it is reasonable to assume data
QQ
came from a normal distribution.
came
Sample Data: n = 10 y = 98.7 s = 2.8694
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 57
University
57 Combustion Engine
(1) State hypotheses, set alpha.
(2) Choose test statistic
(3,4) Designate critical value for test and
draw con...
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 Fall '13
 Wang
 Statistics

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