Unformatted text preview: clusion.
or
Calculate pvalue and draw conclusion.
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 58
University
58 (3) Designate Critical Region
Assumes H0: µ = 100 is true 0.05 4 3 2 1 0
100 4 3 2 1 0 1.833 1 2 +1 +2 3 +3 4
Y=avg hp +4 tdf=9 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 59
University
59 Draw conclusion:
t df =9 4 y − µ0
98.7 − 100
=
=
= −1.4327
s / n 2.8694 / 10 3 2 1 1.4327
1.833 0 1 2 3 4 tdf=9 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 60
University
60 pvalue
The pvalue iis the probability of getting
s
the sample result we got or something
more extreme.
more 0.0928 4 3 2 1 1.4327 0 1 2 3 4 tdf=9 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 61
University
61 pvalue
P(tdf=9 < 1.4327) = 0.0928
P(t
Note:
Note:
If pvalue < α, reject H0.
value
If pvalue > α. Fail to reject H0.
value 0.0928
0.05 4 3 2 1 1.4327
1.833 0 1 2 3 4 tdf=9 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 62
University
62 Average Life of a Light Bulb
Historically, a particular light bulb has
Historically,
had a mean life of no more than 2000
hours. We have changed the
production process and believe that
the life of the bulb has increased.
the
Let µ = mean life.
Let
(1) Set Up Hypotheses α = 0.05 H0:
Ha: G. Baker, Department of Statistics
G.
University of South Carolina; Slide 63
University
63 Average Life of a Light Bulb
(2) Collect Data and calculate test statistic: y = 2141
t df =14 n = 15 s = 216 y − µ 0 2141 − 2000
=
=
= 2.5282
s/ n
216 / 15 0.05
0.0121
4 3 2 1 0 1 2 3 4 tdf=14 1.761 2.5282 pvalue = P(tdf=14 > 2.5282) = 0.0121 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 64
University
64 Average Life of a Light Bulb
State Conclusion:
At 0.05 level of significance there is
At
insufficient evidence to conclude
that µ > 2000 hours.
B. At 0.05 level of significance there is
At
sufficient evidence to conclude that
µ > 2000 hours. A. G. Baker, Department of Statistics
G.
University of South Carolina; Slide 65
University
65 Mean Width of a Manufactured Part
Test the theory that the mean width of a
manufactured part differs from 100 cm.
manufactured
Let µ = mean width.
Let
(1) Set up Hypotheses
(1) α = 0.05 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 66
University
66 Mean Width of a Manufactured Part
(2,3) Collect data and calculate test statistic.
(2,3) Collect y = 105 s = 6 n = 20 t df =19 =
p − value = 2 * P(t df =19 ....
(4) State conclusion.
G. Baker, Department of Statistics
G.
University of South Carolina; Slide 67
University
67 Given population parameter µ and value µ0:
Given
and
For Ho: µ = µ0
For
Ha: µ = µ0 α/2 α/2 Ha H0 Ha: µ > µ0 α
H0 Ha: µ < µ0 Ha Ha α Ha H0 G. Baker, Department of Statistics
G.
University of South Carolina; Slide 68
University
68 There Are Two Errors We Can
There
Make in a Hypothesis Test
Make
1) Reject H0 when H0 iis true. This is call...
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 Fall '13
 Wang
 Statistics, Normal Distribution, Standard Deviation, G. Baker

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