Download Stat 104 – Lecture 19 y Population Distribution of the

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
Document related concepts
no text concepts found
Transcript 
Stat 104 – Lecture 19
Population
• Shape: Looks like a normal model.
• Center:
– Mean, µ = 16
• Spread:
– Standard Deviation, σ = 5
1
Distribution of the
Sample Mean, y
•
•
•
•
n=5
Shape: Normal model
Center: Mean, µ = 16
Spread: Standard Deviation,
SD( y ) =
σ
n
=
5
= 2.24
5
2
Summary
• Sampling from a population that
follows a Normal Model.
• Distribution of the sample mean, y
– Shape: Normal model
– Center: µ
σ
– Spread: SD( y ) =
n
3
1
Stat 104 – Lecture 19
4
Population
• Shape: Skewed right.
• Center:
– Mean, µ = 8.08
• Spread:
– Standard Deviation, σ = 6.22
5
Distribution of the
Sample Mean, y
•
•
•
•
n=5
Shape: Approximately normal
Center: Mean, µ = 8.08
Spread: Standard Deviation,
SD( y ) =
σ
n
=
6.22
= 2.78
5
6
2
Stat 104 – Lecture 19
7
Population
• Shape: Skewed right
• Center:
– Mean, µ = 8.08
• Spread:
– Standard Deviation, σ = 6.22
8
Distribution of the
Sample Mean, y
•
•
•
•
n = 25
Shape: Approximately normal
Center: Mean, µ = 8.08
Spread: Standard Deviation,
SD( y ) =
σ
n
=
6.22
= 1.24
25
9
3
Stat 104 – Lecture 19
Central Limit Theorem
• When selecting random samples
from a population with a
distribution that is not normal, the
distribution of the sample mean, y ,
will be approximately normally
distributed.
10
Central Limit Theorem
• The larger the sample, the closer
the distribution of the sample
mean, y , is to being a normal
model.
11
Summary
• Sampling from a population that
does not follow a Normal Model.
• Distribution of the sample mean, y
– Shape: Approximately normal
– Center: µ
σ
– Spread: SD( y ) =
n
12
4
Related documents