This document is the first chapter of a statistics textbook. It covers basic statistical concepts such as populations and samples, qualitative and quantitative data, methods for describing data both numerically and graphically, the normal probability distribution, sampling distributions, estimating population means, hypothesis testing of population means, comparing differences between population means, and comparing variances between populations. It includes examples and figures to illustrate key statistical techniques.

1. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Chapter 1
A Review of
Basic
Concepts
(Optional)

2. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.1
Statistics and
Data

3. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 3

4. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.2
Populations,
Samples, and
Random
Sampling

5. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 5

6. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.3
Describing
Qualitative
Data

7. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 7

8. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 8

9. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 9
Figure 1.1 SAS bar graph for data on
22 aphasiacs

10. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 10
Figure 1.2 SPSS pie chart for data
on 22 aphasiacs

11. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.4
Describing
Quantitative
Data
Graphically

12. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 12
Figure 1.3 Relative frequency
distribution: IQs of identical twins

13. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 13
Figure 1.4 Probability distribution
for a quantitative variable

14. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 14

15. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 15
Figure 1.5 MINITAB stem-and-leaf
plot for EPA gas mileage

16. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 16
Figure 1.6 SPSS histogram for 100
EPA gas mileage

17. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.5
Describing
Quantitative
Data
Numerically

18. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 18

19. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 19
Figure 1.7 MINITAB printout:
Describing the no-show data, Example
1.6

20. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.6
Normal
Probability
Distribution

21. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 21
Figure 1.8 A normal probability
distribution

22. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 22
Figure 1.9 Several normal distributions
with different means and standard
deviations

23. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 23

24. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 24
Figure 1.10 Normal probability
distribution m = 50, s = 15

25. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 25
Figure 1.11 A distribution of z scores
(a standard normal distribution)

26. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 26
Figure 1.12 Standard normal
distribution: m = 0, s = 1

27. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.7
Sampling
Distributions
and the
Central Limit
Theorem

28. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 28
Figure 1.13 Sampling distributions for
y based on a sample of n = 25
measurements
_

29. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 29
Figure 1.14 Sampling distributions of
x for different populations and different
sample sizes
_

30. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 30
Figure 1.15 A population relative
frequency distribution and the sampling
distribution for y
_

31. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 31
Figure 1.16 The sampling
distribution of y
_

32. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.8
Estimating a
Population
Mean

33. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 33
Figure 1.17 Sampling distribution
of y
_

34. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 34
Figure 1.18 Locating za/2 on the
standard normal curve

35. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 35

36. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 36

37. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 37

38. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 38
Figure 1.19 SAS descriptive statistics
for n = 50 sample attention times

39. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 39
Figure 1.20 The t.025 value in a t
distribution with 4 df and the corresponding
z.025 value

40. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 40

41. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 41

42. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 42
Figure 1.21 MINITAB descriptive statistics
and confidence interval for Example 1.12

43. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.9
Testing a
Hypothesis
About a
Population
Mean

44. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 44
Figure 1.22 The sampling
distribution of y for m = m 0
_

45. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 45
Figure 1.23 Location of the rejection
region for various alternative hypotheses

46. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 46
Figure 1.24 Testing Ha: m >m 0
using a p-value

47. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 47

48. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 48

49. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 49
Figure 1.25 SPSS printout for
Example 1.14

50. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 50

51. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 51

52. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 52
Figure 1.26 Rejection region for
Example 1.15

53. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 53
Figure 1.27 SAS output for
testing benzene mean

54. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.10
Inferences
About the
Difference
Between Two
Population
Means

55. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 55

56. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 56

57. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 57

58. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 58

59. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 59
Figure 1.28 SPSS analysis for diet
study, Example 1.16

60. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 60

61. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 61

62. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 62

63. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 63
Figure 1.29 SAS output for
Example 1.17

64. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 64
Figure 1.30 Rejection region for
Example 1.17

65. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 65

66. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 66

67. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 67
Figure 1.31 Rejection region for
analysis of data in Table 1.17

68. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 68
Figure 1.32 MINITAB paired difference
analysis of data in Table 1.17

69. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 69

70. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 70

71. Copyright © 2012 Pearson Education, Inc. All rights reserved.
Section 1.11
Comparing
Two
Population
Variances

72. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 72
Figure 1.33 An F distribution with 7
and 9 df

73. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 73

74. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 74
Figure 1.34 An F distribution with 7
and 9 df: a = .05

75. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 75
Figure 1.35 Rejection region for
production example F distribution

76. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 76

77. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 77

78. Copyright © 2012 Pearson Education, Inc. All rights reserved.
1- 78
Figure 1.36 SAS F-test for the data
Table 1.19