Stat 104 Lecture 19: Distributions of Sample Means from Populations with Different Shapes , Study notes of Statistics

Information on the distributions of sample means from populations with different shapes - normal, skewed right, and not normal. It includes details on the mean, standard deviation, and shape of the population and sample mean distributions.

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

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Stat 104 – Lecture 19
1
1
Population
Shape: Looks like a normal model.
•Center:
Mean,
•Spread:
Standard Deviation,
16=
µ
5=
σ
2
Distribution of the
Sample Mean,
•n = 5
Shape: Normal model
•Center: Mean,
Spread: Standard Deviation,
y
16=
µ
()
24.2
5
5
SD === n
y
σ
3
Summary
Sampling from a population that
follows a Normal Model.
Distribution of the sample mean,
Shape: Normal model
–Center:
Spread:
y
µ
()
n
y
σ
=SD
pf3
pf4

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1

Population

  • Shape: Looks like a normal model.
  • Center:
    • Mean,
  • Spread:
    • Standard Deviation,

μ= 16

σ= 5

2

Distribution of the

Sample Mean,

  • n = 5
  • Shape: Normal model
  • Center: Mean,
  • Spread: Standard Deviation,

y

μ= 16

SD = =^5 =

n

y^ σ

3

Summary

  • Sampling from a population that follows a Normal Model.
  • Distribution of the sample mean,
    • Shape: Normal model
    • Center:
    • Spread:

y

μ ( ) n

SD y =^ σ

4

5

Population

  • Shape: Skewed right.
  • Center:
    • Mean,
  • Spread:
    • Standard Deviation,

μ= 8. 08

σ= 6. 22

6

Distribution of the

Sample Mean,

  • n = 5
  • Shape: Approximately normal
  • Center: Mean,
  • Spread: Standard Deviation,

y

μ= 8. 08

SD = =^6.^22 =

n

y^ σ

10

Central Limit Theorem

  • When selecting random samples from a population with a distribution that is not normal, the distribution of the sample mean, , will be approximately normally distributed.

y

11

Central Limit Theorem

  • The larger the sample, the closer the distribution of the sample mean, , is to being a normal model.

y

12

Summary

  • Sampling from a population that does not follow a Normal Model.
  • Distribution of the sample mean,
    • Shape: Approximately normal
    • Center:
    • Spread:

y

μ ( ) n

SD y =^ σ