This document summarizes key concepts from Chapter 7 about the sampling distribution of the sample mean. It introduces sampling error that occurs when using a sample to estimate a population characteristic. It defines the sampling distribution of the sample mean as the distribution of the variable for a given sample size. Several figures and outputs show histograms of sampling distributions with superimposed normal curves. The mean and standard deviation of the sampling distribution are discussed. It is noted that as sample size increases, the sampling distribution of the mean approximates the normal distribution according to the central limit theorem.

1. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 1
Chapter 7
The Sampling
Distribution of the
Sample Mean
Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 1

2. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 2
Chapter 7
The Sampling Distribution of
the Sample Mean

3. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 3
Section 7.1
Sampling Error; the Need for
Sampling Distributions

4. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 4
Definition 7.1
Sampling Error
Sampling error is the error resulting from using a
sample to estimate a population characteristic.

5. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 5
Definition 7.2
Sampling Distribution of the Sample Mean
For a variable x and a given sample size, the
distribution of the variable is called the sampling
distribution of the sample mean.
x

6. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 6
Table 7.2
Possible samples
and sample means
for samples of size 2
µ = ∑xi = 76+78+79+ 81+86 = 80
N 5
A, B, C, D, E
76 78 79 81 86
H1

7. Slide 6
H1 HP, 5/9/2020

8. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 7
Figure 7.1
Dotplot for the sampling distribution of the sample mean for
samples of size 2 ( n = 2)

9. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 8
Figure 7.3
Dotplots for the sampling
distributions of the sample
mean for the heights of the five
starting players for samples of
sizes 1, 2, 3, 4, and 5
A, B, C, D, E
76 78 79 81 86

10. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 9
Table 7.4
Sample size and sampling error illustrations for the heights
of the basketball players (“No.” is an abbreviation of
“Number”)

11. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 10
Key Fact 7.1

12. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 11
Section 7.2
The Mean and Standard
Deviation of the Sample Mean

13. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 12
Formula 7.1

14. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 13
Formula 7.2

15. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 14
Section 7.3
The Sampling Distribution of
the Sample Mean

16. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 15
Output 7.1
Histogram of the sample means for 1000 samples of four
IQs with superimposed normal curve

17. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 16
Key Fact 7.2

18. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 17
Figure 7.4
(a) Normal distribution for IQs; (b) sampling distribution of
the sample mean for n = 4; (c) sampling distribution of the
sample mean for n = 16

19. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 18
Key Fact 7.3

20. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 19
Figure 7.5
Relative-frequency histogram for household size

21. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 20
Output 7.2
Histogram of the sample means for 1000 samples of
30 household sizes with superimposed normal curve

22. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 21
Key Fact 7.4

23. Copyright © 2017 Pearson Education, Ltd. Chapter 7, Slide 22
Figure 7.6
Sampling distributions of the sample mean for
(a) normal, (b) reverse-J-shaped, and (c) uniform variables