x z n − =

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SECTION 8-4
TESTING A CLAIM ABOUT A
MEAN: ࣌ KNOWN
Requirements for Testing Claims About
a Population Mean (with σ Known)
The sample is a simple random
sample.
The value of the population standard
deviation is known.
Either or both of these conditions is
satisfied: The population is normally
distributed or n>30.
Test Statistic for Testing a Claim
About a Mean (with σ Known)
z=
x − µx
σ
n
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Example:
Listed below are recorded speeds (in mi/h) of
randomly selected cars traveling on a section of
Highway 405 in Los Angeles (based on data from
Sigalert). That part of the highway has a posted
speed limit of 65 mi/h. Assume that the standard
deviation of speeds is 5.7 mi/h and use a 0.01
significance level to test the claim that the sample
is from a population with a mean that is greater
than 65 mi/h.
68
65
59
60
68
73
75
73
72
66
70
61
73
71
56
75
65
68
66
58
74
74
75
74
73
66
68
60
72
71
75
73
68
65
62
58
65
73
72
75
Example:
Step 1: Create null and alternative
hypothesis
H0: µ = 65 mi/h
H1: µ > 65 mi/h
Example:
Step 2: Calculate the test statistic
and find the p-value.
USING JMP
•Analyze, Distribution
•Test Mean
z = 3.7448
P-Value < .0001
Because lower tailed, then select < from JMP
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Example:
Step 3: Formulate conclusion
The P-Value of .0001 is less than the
significance level of .01. Therefore,
reject H0.
What the final conclusion?
YOUR TURN!
Recap
In this section we have discussed:
Requirements for testing claims
about population means, σ
known.
P-value method. (using JMP)
Traditional method.
3
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SECTION 8-5
TESTING A CLAIM ABOUT A
MEAN: ࣌ NOT KNOWN
Notation
n
x
= sample size
= sample mean
µ x = population mean of all sample means
from sample size n
Requirements for Testing Claims About
a Population Mean (with σ Not Known)
1) The sample is a simple random sample.
2) The value of the population standard
deviation σ is not known.
3) Either or both of these conditions is
satisfied: The population is normally
distributed or n>30.
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Test Statistic for Testing a Claim
About a Mean (with σ Not Known)
t=
x − µx
s
n
EPA investigating gas mileage in advanced hybrid vehicles
http://www.greencarreports.com/news/1080961_consumer-reports-new-ford-hybridsdont-meet-mileage-ratings
Example:
Consumer Reports conducted tests of the gas mileage
for the new Ford Fusion. Listed below are results from
those tests, with the measurements given in miles per
gallon. Ford claims that its combined gas mileage is t
least a47 mpg. Use a 0.01 significance level to test the
claim that the gas mileage in the Ford Fusion is at least
47 miles per gallon.
Do the results warrant an investigation??
Car 1
38.94
Car 2
38.45
Car 3
38.33
Car 4
54.76
Car 5
40.89
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Example:
Step 1: Create null and alternative
hypothesis
H0: ߤ = 47 mpg
H1: ߤ < 47 mpg
Example:
Step 2: Calculate the test statistic
and find the p-value.
USING JMP
•Analyze, Distribution
•Test Mean
t = -1.4978
P-Value = .1043
Example:
Step 3: Formulate conclusion
The P-Value of .1043 is greater than
the significance level of .01. Therefore,
fail to reject H0.
What the final conclusion?
6

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