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Unformatted text preview: niversity of South Carolina; Slide 20
University
20 If the time between industrial accidents
If
follows an exponential distribution with an
average of 700 days, what is the probability
that the average time between 49 pairs of
accidents will be greater than 900 days?
accidents G. Baker, Department of Statistics
G.
University of South Carolina; Slide 21
University
21 XYZ Bottling Company claims that
XYZ
the distribution of fill on it’s 16 oz
the
16
bottles averages 16.2 ounces with
a standard deviation of 0.1 oz. We
randomly sample 36 bottles and
get y = 16.15. If we assume a
standard deviation of 0.1 oz, do we
believe XYZ’s claim of averaging
XYZ claim
16.2 ounces?
16.2
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 22
University
22 Up Until Now We have been Assuming
Up
that We Knew the True Standard
Deviation (σ), But Let’s Face Facts …
Deviation
Face
When we use s to estimate σ, then the
to
then
calculated value
calculated
y−µ s/ n
follows a tdistribution with n1 degrees of
follows
distribution
degrees
freedom.
freedom.
Note: we must be able to assume that we are
Note:
sampling from a normal population.
sampling
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 23
University
23 Let’s take another look at XYZ
take
Bottling Company. If we assume
that fill on the individual bottles
follows a normal distribution, does
the following data support the
claim of an average fill of 16.2 oz?
16.1 16.0 16.3 16.2 16.1
16.1 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 24
University
24 In Summary
When we know σ: y−µ
Z=
σ/ n
When we estimate σ with s:
with y−µ
t df = n −1 =
s/ n We assume we are
sampling from a
normal
population.
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 25
University
25 Relationship Between Z and t
Relationship
Distributions
Distributions
Z
tdf=3
tdf=1 4 3 2 1 0 1 2 3 4 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 26
University
26 Internal Combustion Engine
The nominal power produced by a studentThe
designed internal combustion engine should
designed
be 100 hp. The student team that designed
the engine conducted 10 tests to determine
the actual power. The data follow:
the
98, 101, 102, 97, 101, 98, 100, 92, 98, 100
Assume data came from a normal distribution.
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 27
University
27 Internal Combustion Engine
Summary Data:
Column
hp n Mean
10 Std. Dev. 98.7 2.9 What is the probability of getting a sample
mean of 98.7 hp or less if the true mean is
100 hp?
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 28
University
28 Internal Combustion Engine
98.7 − 100 P ( y ≤ 98.7  µ = 100) = P t df =9 ≤ = P (t df =9 ≤ −1.418)
2.9 / 10 0.0949 4 3 2 1 0 1 2 3 4 t(df=9) What did we assume when doing this analysis?
G. Baker, Department of Statistics
G. Are you comfortable with the assumption?University of South Caroli...
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 Fall '13
 Wang
 Statistics

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