Stat 104 – Lecture 24
Chapters 8 and 9
Quantitative variable
Population Parameters: 
Population
Inference
Sample
Sample Mean
y
1
Example
• What is the mean alcohol
content of beer?
• A random sample of 10 beers
is taken and the alcohol
content (%) is measured.
2
• Population – all beers.
• Variable – alcohol content, %.
• Parameter – mean alcohol
content of beer.
3
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Stat 104 – Lecture 24
Sample Data – Alcohol (%)
Molson
Canadian
Michelob
Dark
Big Barrel
Lager
Hamm’s
5.19
Tsingtao
4.79
4.76
4.32
4.53
Heineken
Dark
O’Keefe
Canadian
Olympia
Lager
Miller
Draft
Guinness
Stout
5.17
4.96
4.78
4.85
4.27
4
Sample Summary
• Sample size:
–n = 10
• Sample mean:
– y = 4.762
• Sample standard deviation:
–s = 0.314
5
Sampling Distribution of y
Quantitative variable
Population Parameters: , 
Population
Sample Sample
Mean,
y
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2
Stat 104 – Lecture 24
Summary
• Sampling from a population that
follows a Normal Model.
• Distribution of the sample mean, y
–Shape: Normal model
–Center: 

–Spread: SD y  
n
7
Unknown, 
• If we do not know the value
of the population standard
deviation we cannot
standardize and cannot use
table Z.
8
Unknown,
• We can use the sample
standard deviation, s, as an
estimate of the population
standard deviation,  .
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3
Stat 104 – Lecture 24
Unknown, 
• We can NOT continue to use
the standard normal
distribution or Table Z.
• Why?
10
11
12
4
Stat 104 – Lecture 24
95% Confidence?
• Simulation illustrating
repeating the procedure.
• http://www.rossmanchance.com/a
pplets/NewConfsim/Confsim.html
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14
Quantitative Variable
• Confidence Interval for  .
 s 
 s 
y  t* 
 to y  t * 

 n
 n
• t* found in Table T, df = n – 1
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5
Stat 104 – Lecture 24
Quantitative variable
• Test statistic.
t
y
, Table T  P - value
 s 


 n
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Confidence Interval for 
 s 
 s 
y  t* 
 to y  t * 

n
n




df  n  1
17
Inference for 
• Do NOT use Table Z!
Table Z
• Use Table T instead!
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