文档介绍：CHAPTER 8: Sampling Distributions
to pany
Introduction to Business Statistics
fourth edition, by Ronald M. Weiers
Presentation by Priscilla Chaffe-Stengel
Donald N. Stengel
© 2002 The Wadsworth Group
Chapter 8 - Learning Objectives
Determine the sampling distributions of:
Means.
Proportions.
Explain the Central Limit Theorem.
Determine the effect on the sampling distribution when the samples are relatively pared to the population from which they are drawn.
© 2002 The Wadsworth Group
Sampling Distribution of the Mean
When the population is normally distributed
Shape: Regardless of sample size, the distribution of sample means will be normally distributed.
Center: The mean of the distribution of sample means is the mean of the population. Sample size does not affect the center of the distribution.
Spread: The standard deviation of the distribution of sample means, or the standard error, is
.
n
x
s
s
=
© 2002 The Wadsworth Group
Standardizing a Sample Mean on a Normal Curve
The standardized z-score is how far above or below the sample mean pared to the population mean in units of standard error.
“How far above or below”= sample mean minus µ
“In units of standard error”= divide by
Standardized sample mean
n
x
z
s
m
=
m
-
=
–
error
standard
mean
sample
n
s
© 2002 The Wadsworth Group
Central Limit Theorem
According to the Central Limit Theorem (CLT), the larger the sample size, the more normal the distribution of sample means es. The CLT is central to the concept of statistical inference because it permits us to draw conclusions about the population based strictly on sample data without having knowledge about the distribution of the underlying population.
© 2002 The Wadsworth Group
Sampling Distribution of the Mean
When the population is not normally distributed
Shape: When the sample size taken from such a population is sufficiently large, the distribution of its sample means will be approximately normally distributed regardles