Download Chapter 7: The Sampling Distribution of the Sample Mean

Chapter 7: The Sampling
Distribution of the Sample Mean
7.1
Sampling Error
The Need for Sampling Distributions
Sampling Error
• Error resulting from using a sample to
estimate a population characteristic
Sampling Distribution of the Sample Mean
• For a variable x and a given sample size
• The distribution of all possible sample means
Example 7.2
• Suppose that the population of interest consists of the five
starting players on a men’s basketball team whom, for
convenience, we will call A, B, C, D, and E. Further suppose
that the variable of interest is height, in inches.
Player
A
B
C
D
E
Height
76
78
79
81
86
• A. Obtain the sampling distribution of the sample mean for
samples of size 2.
Example 7.2
• Suppose that the population of interest consists of the five
starting players on a men’s basketball team whom, for
convenience, we will call A, B, C, D, and E. Further suppose
that the variable of interest is height, in inches.
Player
A
B
C
D
E
Height
76
78
79
81
86
• B. Make some observations about sampling error when
the mean height of a random sample of two players is used
to estimate the population mean height.
Example 7.2
• Suppose that the population of interest consists of the five starting
players on a men’s basketball team whom, for convenience, we will
call A, B, C, D, and E. Further suppose that the variable of interest is
height, in inches.
Player
A
B
C
D
E
Height
76
78
79
81
86
• C. Find the probability that, for a random sample of size 2, the
sampling error made in estimating the population mean by the
sample mean will be 1 inch or less (determine the probability that
xbar will be within 1 inch of μ)
Example 7.3
• For the same basketball players:
Player
A
B
C
D
E
Height
76
78
79
81
86
• A. Obtain the sampling distribution of the sample
mean for samples of size 4.
Example 7.3
• For the same basketball players:
Player
A
B
C
D
E
Height
76
78
79
81
86
• B. Make some observations about sampling error
when the mean height of a random sample of four
players is used to estimate the population mean
height.
Example 7.3
• For the same basketball players:
Player
A
B
C
D
E
Height
76
78
79
81
86
• C. Find the probability that, for a random sample of
size 4, the sampling error made in estimating the
population mean by the sample mean will be 1 inch
or less.
Sample Size & Sampling Error
• The possible sample means cluster more
closely around the population mean as sample
size increases.
• The larger the sample size, the smaller the
sampling error tends to be in estimating a
population mean from a sample mean.
Homework
• P. 317
• 1 – 15