Ebook Elementary statistics: A step by step approach (Eighth edition) - Part 1

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Important Formulas
Chapter 3 Data Description
᎐

Mean for individual data: X ϭ
᎐

Mean for grouped data: X ϭ

Chapter 5 Discrete Probability Distributions
͚X
n

͚ f • Xm
n

͙

͚Θ X Ϫ X Ι 2
nϪ1

͙

nΘ ͚X 2Ι Ϫ Θ͚XΙ 2
nΘn Ϫ 1Ι
(Shortcut formula)

sϭ

or

Standard deviation for grouped data:
sϭ

͙

nΘ͚ f • X m2 Ι Ϫ Θ ͚ f • Xm Ι 2
nΘn Ϫ 1Ι

Range rule of thumb: s Ϸ

s2 ϭ ͚[X 2 и P(X)] Ϫ m2
s ϭ ͙͚[X 2 • PΘXΙ ] Ϫ m2

Standard deviation for a sample:
sϭ

Mean for a probability distribution: m ϭ ͚[X и P(X)]
Variance and standard deviation for a probability
distribution:

range
4

n!
• pX • q nϪX
Ϫ XΙ !X!

Mean for binomial distribution: m ϭ n и p
Variance and standard deviation for the binomial
distribution: s2 ϭ n и p и q
s ϭ ͙n • p • q
Multinomial probability:
n!
PΘXΙ ϭ
• p X 1 • p2X 2 • p3X 3 • • • pkX k
X1!X2!X3! . . . Xk! 1
Binomial probability: PΘXΙ ϭ

Θn

Poisson probability: P(X; l) ϭ

Chapter 4 Probability and Counting Rules
Addition rule 1 (mutually exclusive events):
P(A or B) ϭ P(A) ϩ P(B)
Addition rule 2 (events not mutually exclusive):
P(A or B) ϭ P(A) ϩ P(B) Ϫ P(A and B)
Multiplication rule 1 (independent events):
P(A and B) ϭ P(A) и P(B)
Multiplication rule 2 (dependent events):
P(A and B) ϭ P(A) и P(B ͉ A)
Conditional probability: PΘB Խ AΙ ϭ

Expectation: E(X) ϭ ͚[X и P(X)]

PΘ A and BΙ
PΘ AΙ

᎐

Complementary events: P(E ) ϭ 1 Ϫ P(E)
Fundamental counting rule: Total number of outcomes
of a sequence when each event has a different
number of possibilities: k 1 и k 2 и k 3 и и и k n
Permutation rule: Number of permutations of n objects
n!
taking r at a time is n Pr ϭ
Θn Ϫ rΙ !
Combination rule: Number of combinations of r objects
n!
selected from n objects is n Cr ϭ
Θ n Ϫ r Ι !r!

X ϭ 0, 1, 2, . . .

e Ϫ ␭␭X
where
X!

Hypergeometric probability: PΘXΙ ϭ a

CX • bCnϪX
aϩbCn

Chapter 6 The Normal Distribution
Standard score z ϭ

᎐

XϪ␮
␴

zϭ

or

XϪX
s

Mean of sample means: mX ϭ m

␴
͙n
᎐
XϪ␮
Central limit theorem formula: z ϭ
␴ ր͙n
Standard error of the mean: sX ϭ

Chapter 7 Confidence Intervals and Sample
Size
z confidence interval for means:
᎐

X Ϫ z ␣ր2

Θ ͙␴n Ι Ͻ ␮ Ͻ X ϩ z ր Θ ͙␴n Ι

᎐

␣ 2

t confidence interval for means:
᎐

X Ϫ t ␣ր2

Θ ͙s n Ι Ͻ ␮ Ͻ X ϩ t ր Θ ͙s n Ι
᎐

␣ 2

z␣ր2 • ␴
E
maximum error of estimate

Sample size for means: n ϭ

Θ

Ι

2

where E is the

Confidence interval for a proportion:
pˆ Ϫ Θz ␣ ր 2 Ι

͙

pˆ qˆ
Ͻ p Ͻ pˆ ϩ Θz ␣ ր 2Ι
n

͙

pˆ qˆ
n


Sample size for a proportion: n ϭ pˆ qˆ

z␣ 2

Θ Eր Ι

2

Formula for the confidence interval for difference of two
means (small independent samples, variance
unequal):

X
and
qˆ ϭ 1 Ϫ pˆ
n
Confidence interval for variance:

pˆ ϭ

where

Θn

᎐

Θ X1

͙

᎐

Ϫ X2Ι Ϫ t ␣ ր 2

Θ n Ϫ 1 Ι s2
Ϫ 1Ι s2
Ͻ ␴2 Ͻ
2
␹ right
␹ 2left

᎐

͙

Ϫ 1Ι s2
Ͻ␴Ͻ
␹ 2right

͙

Θn

᎐

tϭ

᎐

XϪ␮
for any value n. If n Ͻ 30,
␴ ր͙n
population must be normally distributed.

sD ϭ

(d.f. ϭ n Ϫ 1)

Θn

Ϫ 1Ι s 2
␴2

᎐

᎐

Ϫ X2Ι Ϫ z␣ր2

͙

␴ 21 ␴ 22
ϩ
Ͻ ␮1 Ϫ ␮ 2
n1
n2
᎐

᎐

᎐

᎐

Ϫ X2 Ι Ϫ Θ␮1 Ϫ ␮ 2Ι

͙

͙

__

pq

Θ n1 ϩ n1 Ι
1

_

pϭ

2

X1 ϩ X2
n1 ϩ n2

_

_

qϭ1Ϫp

pˆ 1 ϭ

X1
n1

pˆ2 ϭ

X2
n2

s21 s22
ϩ
n1 n2

(d.f. ϭ the smaller of n 1 Ϫ 1 or n2 Ϫ 1)

Θ pˆ1

Ϫ pˆ2Ι Ϫ z␣ր2

͙

pˆ 1 qˆ1 pˆ 2 qˆ2
ϩ
Ͻ p1 Ϫ p2
n1
n2

Ͻ Θ pˆ1 Ϫ pˆ 2Ι ϩ z␣ ր 2

͙

␴ 21 ␴ 22
ϩ
n1
n2

t test for comparing two means (independent samples,
variances not equal):
Θ X1

Ϫ pˆ 2Ι Ϫ Θ p1 Ϫ p2Ι

Formula for the confidence interval for the difference of
two proportions:

Ͻ ΘX1 Ϫ X2Ι ϩ z ␣ ր 2

tϭ

Θ pˆ1

where

Ϫ Θ ␮1 Ϫ ␮ 2 Ι

␴ 21 ␴ 22
ϩ
n1
n2

Formula for the confidence interval for difference of two
means (large samples):
Θ X1

ϭ n Ϫ 1Ι

z test for comparing two proportions:

z test for comparing two means (independent samples):

͙

Θ d.f.

and

SD
S
᎐
Ͻ ␮D Ͻ D ϩ t␣ր2 D
͙n
͙n
(d.f. ϭ n Ϫ 1)

zϭ

Chapter 9 Testing the Difference Between
Two Means, Two Proportions,
and Two Variances
Ϫ

n͚D 2 Ϫ Θ͚DΙ 2
nΘn Ϫ 1Ι

͚D
n

᎐

Dϭ

᎐

(d.f. ϭ n Ϫ 1)

zϭ

͙

where

D Ϫ t␣ր2

pˆ Ϫ p
͙pqրn

Chi-square test for a single variance: ␹ 2 ϭ

᎐
X2 Ι

D Ϫ ␮D
sD ր͙n

Formula for confidence interval for the mean of the
difference for dependent samples:

᎐

᎐
Θ X1

s21 s22
ϩ
n1 n2

t test for comparing two means for dependent samples:

z test: z ϭ

z test for proportions: z ϭ

͙

(d.f. ϭ smaller of n1 Ϫ 1 and n2 Ϫ 1)

Ϫ 1Ι s2
␹ 2left

Chapter 8 Hypothesis Testing

XϪ␮
t test: t ϭ
sր͙n

᎐

Ͻ ΘX1 Ϫ X2Ι ϩ t ␣ ր 2

Confidence interval for standard deviation:
Θn

s21 s22
ϩ Ͻ ␮1 Ϫ ␮ 2
n1 n2

͙

pˆ 1 qˆ1 pˆ 2 qˆ2
ϩ
n1
n2

s21
where s 21 is the
s22
larger variance and d.f.N. ϭ n1 Ϫ 1, d.f.D. ϭ n2 Ϫ 1

F test for comparing two variances: F ϭ


Chapter 10 Correlation and Regression

Chapter 11 Other Chi-Square Tests

Correlation coefficient:

Chi-square test for goodness-of-fit:

rϭ

nΘ͚xyΙ Ϫ Θ ͚xΙΘ͚yΙ

t test for correlation coefficient: t ϭ r
(d.f. ϭ n Ϫ 2)

͙

nϪ2
1 Ϫ r2

The regression line equation: yЈ ϭ a ϩ bx

Ϫ EΙ 2
E
[d.f. ϭ (rows Ϫ 1)(col. Ϫ 1)]

Ϫ Θ͚xΙΘ͚xyΙ
nΘ͚x2Ι Ϫ Θ͚xΙ 2

nΘ͚xyΙ Ϫ Θ͚xΙΘ͚yΙ
nΘ ͚x 2Ι Ϫ Θ͚xΙ 2

bϭ

Coefficient of determination: r 2 ϭ

͙

explained variation
total variation

ANOVA test: F ϭ
d.f.N. ϭ k Ϫ 1
d.f.D. ϭ N Ϫ k

͚y2 Ϫ a ͚y Ϫ b ͚xy
nϪ2

͙

᎐

1
nΘ x Ϫ X Ι 2
1ϩ ϩ
n n ͚x 2 Ϫ Θ ͚xΙ 2

Ͻ y Ͻ yЈ ϩ t␣ ր 2s est

͙

᎐

1
nΘ x Ϫ XΙ 2
1ϩ ϩ
n n ͚x2 Ϫ Θ͚xΙ 2

(d.f. ϭ n Ϫ 2)
Formula for the multiple correlation coefficient:
Rϭ

͙

2
2
r yx
ϩ r yx
Ϫ 2ryx 1 • ryx 2 • rx 1x2
1
2
1 Ϫ r 2x 1 x 2

Formula for the F test for the multiple correlation
coefficient:
Fϭ

Θ1

Ϫ

R 2րk
ր Ϫ k Ϫ 1Ι

R 2Ι Θn

͚niΘXi Ϫ XGM Ι 2
kϪ1

sW2 ϭ

͚Θni Ϫ 1Ι s2i
͚Θni Ϫ 1Ι

Scheffé test: FS ϭ

Θ1

΄

Ϫ R2 ΙΘn Ϫ 1Ι
nϪkϪ1

Xi Ϫ Xj
͙sW2 րn
Formulas for two-way ANOVA:
SSA
aϪ1
SSB
MSB ϭ
bϪ1
MSA ϭ

MSW ϭ

΅

and

Tukey test: q ϭ

(d.f.N. ϭ n Ϫ k and d.f.D. ϭ n Ϫ k Ϫ 1)

R 2adj ϭ 1 Ϫ

Ϫ Xj Ι 2
րni ϩ 1րnjΙ

ΘXi

sW2 Θ1

FЈ ϭ (k Ϫ 1)(C.V.)

MSAϫB ϭ

Formula for the adjusted R2:

sB2
͚X
where
XGM ϭ
sW2
N
where
N ϭ n1 ϩ n2 ϩ и и и ϩ nk
where
k ϭ number of groups

sB2 ϭ

Prediction interval for y:
yЈ Ϫ t␣ ր 2 sest

ΘO

Chapter 12 Analysis of Variance

Standard error of estimate:
sest ϭ

ΘO

Chi-square test for independence and homogeneity of
proportions:
x2 ϭ a

Θ ͚y ΙΘ ͚x2 Ι

aϭ

where

Ϫ EΙ 2
E
(d.f. ϭ no. of categories Ϫ 1)
x2 ϭ a

͙[nΘ͚x2 Ι Ϫ Θ͚xΙ 2][nΘ ͚y2Ι Ϫ Θ ͚yΙ 2]

Θa

SSAϫB
Ϫ 1ΙΘb Ϫ 1Ι

SSW
abΘ n Ϫ 1Ι

MSA
MSW
MSB
FB ϭ
MSW
FA ϭ

FAϫB ϭ

MSAϫB
MSW


Chapter 13 Nonparametric Statistics
ϩ 0.5Ι Ϫ Θnր2Ι
z test value in the sign test: z ϭ
͙n ր 2
where n ϭ sample size (greater than or equal to 26)
X ϭ smaller number of ϩ or Ϫ signs

Kruskal-Wallis test:

ΘX

Wilcoxon rank sum test: z ϭ

R Ϫ mR
sR

where

␮R ϭ

n1Θn1 ϩ n2 ϩ 1Ι
2

͙

n 1 n 2Θn1 ϩ n 2 ϩ 1Ι
12
R ϭ sum of the ranks for the smaller sample
size (n1)
n1 ϭ smaller of the sample sizes
n2 ϭ larger of the sample sizes
n1 Ն 10 and n2 Ն 10

␴R ϭ

ws Ϫ

Wilcoxon signed-rank test: z ϭ
A
where

nΘn ϩ 1Ι
4

nΘn ϩ 1ΙΘ2n ϩ 1Ι
24

Hϭ

R21 R22
12
R2
ϩ ϩ • • • ϩ k Ϫ 3ΘN ϩ 1Ι
NΘN ϩ 1Ι n1 n2
nk

Θ

Ι

where
R1 ϭ sum of the ranks of sample 1
n1 ϭ size of sample 1
R2 ϭ sum of the ranks of sample 2
n2 ϭ size of sample 2
и
и
и
Rk ϭ sum of the ranks of sample k
nk ϭ size of sample k
N ϭ n1 ϩ n2 ϩ и и и ϩ nk
k ϭ number of samples
Spearman rank correlation coefficient:

rS ϭ 1 Ϫ

6 ͚d 2
nΘn2 Ϫ 1Ι

where
d ϭ difference in the ranks
n ϭ number of data pairs

n ϭ number of pairs where the difference is not 0
ws ϭ smaller sum in absolute value of the signed
ranks

Procedure Table

Step 1

State the hypotheses and identify the claim.

Step 2

Find the critical value(s) from the appropriate table in Appendix C.

Step 3

Compute the test value.

Step 4

Make the decision to reject or not reject the null hypothesis.

Step 5

Summarize the results.

Procedure Table

Solving Hypothesis-Testing Problems (P-value Method)
Step 1

State the hypotheses and identify the claim.

Step 2

Compute the test value.

Step 3

Find the P-value.

Step 4

Make the decision.

Step 5

Summarize the results.

ISBN-13: 978–0–07–743861–6
ISBN-10: 0–07–743861–2

Solving Hypothesis-Testing Problems (Traditional Method)


Table E

The Standard Normal Distribution

Cumulative Standard Normal Distribution
z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

Ϫ3.4

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0002

Ϫ3.3

.0005

.0005

.0005

.0004

.0004

.0004

.0004

.0004

.0004

.0003

Ϫ3.2

.0007

.0007

.0006

.0006

.0006

.0006

.0006

.0005

.0005

.0005

Ϫ3.1

.0010

.0009

.0009

.0009

.0008

.0008

.0008

.0008

.0007

.0007

Ϫ3.0

.0013

.0013

.0013

.0012

.0012

.0011

.0011

.0011

.0010

.0010

Ϫ2.9

.0019

.0018

.0018

.0017

.0016

.0016

.0015

.0015

.0014

.0014

Ϫ2.8

.0026

.0025

.0024

.0023

.0023

.0022

.0021

.0021

.0020

.0019

Ϫ2.7

.0035

.0034

.0033

.0032

.0031

.0030

.0029

.0028

.0027

.0026

Ϫ2.6

.0047

.0045

.0044

.0043

.0041

.0040

.0039

.0038

.0037

.0036

Ϫ2.5

.0062

.0060

.0059

.0057

.0055

.0054

.0052

.0051

.0049

.0048

Ϫ2.4

.0082

.0080

.0078

.0075

.0073

.0071

.0069

.0068

.0066

.0064

Ϫ2.3

.0107

.0104

.0102

.0099

.0096

.0094

.0091

.0089

.0087

.0084

Ϫ2.2

.0139

.0136

.0132

.0129

.0125

.0122

.0119

.0116

.0113

.0110

Ϫ2.1

.0179

.0174

.0170

.0166

.0162

.0158

.0154

.0150

.0146

.0143

Ϫ2.0

.0228

.0222

.0217

.0212

.0207

.0202

.0197

.0192

.0188

.0183

Ϫ1.9

.0287

.0281

.0274

.0268

.0262

.0256

.0250

.0244

.0239

.0233

Ϫ1.8

.0359

.0351

.0344

.0336

.0329

.0322

.0314

.0307

.0301

.0294

Ϫ1.7

.0446

.0436

.0427

.0418

.0409

.0401

.0392

.0384

.0375

.0367

Ϫ1.6

.0548

.0537

.0526

.0516

.0505

.0495

.0485

.0475

.0465

.0455

Ϫ1.5

.0668

.0655

.0643

.0630

.0618

.0606

.0594

.0582

.0571

.0559

Ϫ1.4

.0808

.0793

.0778

.0764

.0749

.0735

.0721

.0708

.0694

.0681

Ϫ1.3

.0968

.0951

.0934

.0918

.0901

.0885

.0869

.0853

.0838

.0823

Ϫ1.2

.1151

.1131

.1112

.1093

.1075

.1056

.1038

.1020

.1003

.0985

Ϫ1.1

.1357

.1335

.1314

.1292

.1271

.1251

.1230

.1210

.1190

.1170

Ϫ1.0

.1587

.1562

.1539

.1515

.1492

.1469

.1446

.1423

.1401

.1379

Ϫ0.9

.1841

.1814

.1788

.1762

.1736

.1711

.1685

.1660

.1635

.1611

Ϫ0.8

.2119

.2090

.2061

.2033

.2005

.1977

.1949

.1922

.1894

.1867

Ϫ0.7

.2420

.2389

.2358

.2327

.2296

.2266

.2236

.2206

.2177

.2148

Ϫ0.6

.2743

.2709

.2676

.2643

.2611

.2578

.2546

.2514

.2483

.2451

Ϫ0.5

.3085

.3050

.3015

.2981

.2946

.2912

.2877

.2843

.2810

.2776

Ϫ0.4

.3446

.3409

.3372

.3336

.3300

.3264

.3228

.3192

.3156

.3121

Ϫ0.3

.3821

.3783

.3745

.3707

.3669

.3632

.3594

.3557

.3520

.3483

Ϫ0.2

.4207

.4168

.4129

.4090

.4052

.4013

.3974

.3936

.3897

.3859

Ϫ0.1

.4602

.4562

.4522

.4483

.4443

.4404

.4364

.4325

.4286

.4247

Ϫ0.0

.5000

.4960

.4920

.4880

.4840

.4801

.4761

.4721

.4681

.4641

For z values less than Ϫ3.49, use 0.0001.
Area

z

0


Table E

(continued )

Cumulative Standard Normal Distribution
z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0

.5000

.5040

.5080

.5120

.5160

.5199

.5239

.5279

.5319

.5359

0.1

.5398

.5438

.5478

.5517

.5557

.5596

.5636

.5675

.5714

.5753

0.2

.5793

.5832

.5871

.5910

.5948

.5987

.6026

.6064

.6103

.6141

0.3

.6179

.6217

.6255

.6293

.6331

.6368

.6406

.6443

.6480

.6517

0.4

.6554

.6591

.6628

.6664

.6700

.6736

.6772

.6808

.6844

.6879

0.5

.6915

.6950

.6985

.7019

.7054

.7088

.7123

.7157

.7190

.7224

0.6

.7257

.7291

.7324

.7357

.7389

.7422

.7454

.7486

.7517

.7549

0.7

.7580

.7611

.7642

.7673

.7704

.7734

.7764

.7794

.7823

.7852

0.8

.7881

.7910

.7939

.7967

.7995

.8023

.8051

.8078

.8106

.8133

0.9

.8159

.8186

.8212

.8238

.8264

.8289

.8315

.8340

.8365

.8389

1.0

.8413

.8438

.8461

.8485

.8508

.8531

.8554

.8577

.8599

.8621

1.1

.8643

.8665

.8686

.8708

.8729

.8749

.8770

.8790

.8810

.8830

1.2

.8849

.8869

.8888

.8907

.8925

.8944

.8962

.8980

.8997

.9015

1.3

.9032

.9049

.9066

.9082

.9099

.9115

.9131

.9147

.9162

.9177

1.4

.9192

.9207

.9222

.9236

.9251

.9265

.9279

.9292

.9306

.9319

1.5

.9332

.9345

.9357

.9370

.9382

.9394

.9406

.9418

.9429

.9441

1.6

.9452

.9463

.9474

.9484

.9495

.9505

.9515

.9525

.9535

.9545

1.7

.9554

.9564

.9573

.9582

.9591

.9599

.9608

.9616

.9625

.9633

1.8

.9641

.9649

.9656

.9664

.9671

.9678

.9686

.9693

.9699

.9706

1.9

.9713

.9719

.9726

.9732

.9738

.9744

.9750

.9756

.9761

.9767

2.0

.9772

.9778

.9783

.9788

.9793

.9798

.9803

.9808

.9812

.9817

2.1

.9821

.9826

.9830

.9834

.9838

.9842

.9846

.9850

.9854

.9857

2.2

.9861

.9864

.9868

.9871

.9875

.9878

.9881

.9884

.9887

.9890

2.3

.9893

.9896

.9898

.9901

.9904

.9906

.9909

.9911

.9913

.9916

2.4

.9918

.9920

.9922

.9925

.9927

.9929

.9931

.9932

.9934

.9936

2.5

.9938

.9940

.9941

.9943

.9945

.9946

.9948

.9949

.9951

.9952

2.6

.9953

.9955

.9956

.9957

.9959

.9960

.9961

.9962

.9963

.9964

2.7

.9965

.9966

.9967

.9968

.9969

.9970

.9971

.9972

.9973

.9974

2.8

.9974

.9975

.9976

.9977

.9977

.9978

.9979

.9979

.9980

.9981

2.9

.9981

.9982

.9982

.9983

.9984

.9984

.9985

.9985

.9986

.9986

3.0

.9987

.9987

.9987

.9988

.9988

.9989

.9989

.9989

.9990

.9990

3.1

.9990

.9991

.9991

.9991

.9992

.9992

.9992

.9992

.9993

.9993

3.2

.9993

.9993

.9994

.9994

.9994

.9994

.9994

.9995

.9995

.9995

3.3

.9995

.9995

.9995

.9996

.9996

.9996

.9996

.9996

.9996

.9997

3.4

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9998

For z values greater than 3.49, use 0.9999.
Area

0

z


Table F

d.f.

The t Distribution
Confidence

intervals

80%

90%

95%

98%

99%

One tail, A

0.10

0.05

0.025

0.01

0.005

Two tails, A

1
2
3
4

5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
32
34
36
38

40
45
50
55
60
65
70
75
80
90
100
500
1000
(z) ϱ

0.20

0.10

0.05

0.02

0.01

3.078
1.886
1.638
1.533
1.476

1.440
1.415
1.397
1.383
1.372
1.363
1.356
1.350
1.345
1.341
1.337
1.333
1.330
1.328
1.325
1.323
1.321
1.319
1.318
1.316
1.315
1.314
1.313
1.311
1.310
1.309
1.307
1.306
1.304
1.303

1.301
1.299
1.297
1.296
1.295
1.294
1.293
1.292
1.291
1.290
1.283
1.282
1.282a

6.314
2.920
2.353
2.132
2.015
1.943
1.895
1.860
1.833
1.812
1.796
1.782
1.771
1.761
1.753
1.746

1.740
1.734
1.729
1.725
1.721
1.717
1.714
1.711
1.708
1.706
1.703
1.701
1.699
1.697
1.694
1.691
1.688
1.686
1.684
1.679
1.676
1.673
1.671
1.669
1.667
1.665
1.664
1.662
1.660
1.648

1.646
1.645b

12.706
4.303
3.182
2.776
2.571
2.447
2.365
2.306
2.262
2.228
2.201
2.179
2.160
2.145
2.131
2.120
2.110
2.101
2.093
2.086
2.080
2.074
2.069
2.064
2.060
2.056
2.052

2.048
2.045
2.042
2.037
2.032
2.028
2.024
2.021
2.014
2.009
2.004
2.000
1.997
1.994
1.992
1.990
1.987
1.984
1.965
1.962
1.960

31.821
6.965
4.541
3.747
3.365
3.143
2.998
2.896

2.821
2.764
2.718
2.681
2.650
2.624
2.602
2.583
2.567
2.552
2.539
2.528
2.518
2.508
2.500
2.492
2.485
2.479
2.473
2.467
2.462
2.457
2.449
2.441
2.434
2.429
2.423
2.412
2.403
2.396

2.390
2.385
2.381
2.377
2.374
2.368
2.364
2.334
2.330
2.326c

63.657
9.925
5.841
4.604
4.032
3.707
3.499
3.355
3.250
3.169
3.106
3.055
3.012
2.977
2.947
2.921
2.898
2.878
2.861

2.845
2.831
2.819
2.807
2.797
2.787
2.779
2.771
2.763
2.756
2.750
2.738
2.728
2.719
2.712
2.704
2.690
2.678
2.668
2.660
2.654
2.648
2.643
2.639
2.632
2.626
2.586
2.581
2.576d

a

This value has been rounded to 1.28 in the textbook.
This value has been rounded to 1.65 in the textbook.
c
This value has been rounded to 2.33 in the textbook.
d
This value has been rounded to 2.58 in the textbook.

One tail

Two tails

b

Source: Adapted from W. H. Beyer, Handbook of Tables for
Probability and Statistics, 2nd ed., CRC Press, Boca Raton,
Fla., 1986. Reprinted with permission.

Area
␣

t

Area
␣
2
Ϫt

Area

␣
2
ϩt


Table G

The Chi-Square Distribution
A

Degrees of
freedom

0.995

0.99

0.975

0.95

0.90

0.10

0.05

0.025

0.01

0.005

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

28
29
30
40
50
60
70
80
90
100

—
0.010
0.072
0.207
0.412
0.676
0.989
1.344
1.735
2.156
2.603
3.074
3.565
4.075
4.601
5.142
5.697
6.265
6.844

7.434
8.034
8.643
9.262
9.886
10.520
11.160
11.808
12.461
13.121
13.787
20.707
27.991
35.534
43.275
51.172
59.196
67.328

—
0.020
0.115
0.297
0.554
0.872
1.239
1.646
2.088
2.558
3.053

3.571
4.107
4.660
5.229
5.812
6.408
7.015
7.633
8.260
8.897
9.542
10.196
10.856
11.524
12.198
12.879
13.565
14.257
14.954
22.164
29.707
37.485
45.442
53.540
61.754
70.065

0.001
0.051
0.216

0.484
0.831
1.237
1.690
2.180
2.700
3.247
3.816
4.404
5.009
5.629
6.262
6.908
7.564
8.231
8.907
9.591
10.283
10.982
11.689
12.401
13.120
13.844
14.573
15.308
16.047
16.791
24.433
32.357
40.482

48.758
57.153
65.647
74.222

0.004
0.103
0.352
0.711
1.145
1.635
2.167
2.733
3.325
3.940
4.575
5.226
5.892
6.571
7.261
7.962
8.672
9.390
10.117
10.851
11.591
12.338
13.091
13.848
14.611

15.379
16.151
16.928
17.708
18.493
26.509
34.764
43.188
51.739
60.391
69.126
77.929

0.016
0.211
0.584
1.064
1.610
2.204
2.833
3.490
4.168
4.865
5.578
6.304
7.042
7.790
8.547
9.312
10.085

10.865
11.651
12.443
13.240
14.042
14.848
15.659
16.473
17.292
18.114
18.939
19.768
20.599
29.051
37.689
46.459
55.329
64.278
73.291
82.358

2.706
4.605
6.251
7.779
9.236
10.645
12.017
13.362
14.684

15.987
17.275
18.549
19.812
21.064
22.307
23.542
24.769
25.989
27.204
28.412
29.615
30.813
32.007
33.196
34.382
35.563
36.741
37.916
39.087
40.256
51.805
63.167
74.397
85.527
96.578
107.565
118.498

3.841

5.991
7.815
9.488
11.071
12.592
14.067
15.507
16.919
18.307
19.675
21.026
22.362
23.685
24.996
26.296
27.587
28.869
30.144
31.410
32.671
33.924
35.172
36.415
37.652
38.885
40.113
41.337
42.557
43.773
55.758

67.505
79.082
90.531
101.879
113.145
124.342

5.024
7.378
9.348
11.143
12.833
14.449
16.013
17.535
19.023
20.483
21.920
23.337
24.736
26.119
27.488
28.845
30.191
31.526
32.852
34.170
35.479
36.781
38.076

39.364
40.646
41.923
43.194
44.461
45.722
46.979
59.342
71.420
83.298
95.023
106.629
118.136
129.561

6.635
9.210
11.345
13.277
15.086
16.812
18.475
20.090
21.666
23.209
24.725
26.217
27.688
29.141
30.578

32.000
33.409
34.805
36.191
37.566
38.932
40.289
41.638
42.980
44.314
45.642
46.963
48.278
49.588
50.892
63.691
76.154
88.379
100.425
112.329
124.116
135.807

7.879
10.597
12.838
14.860
16.750
18.548
20.278

21.955
23.589
25.188
26.757
28.299
29.819
31.319
32.801
34.267
35.718
37.156
38.582
39.997
41.401
42.796
44.181
45.559
46.928
48.290
49.645
50.993
52.336
53.672
66.766
79.490
91.952
104.215
116.321
128.299
140.169

Source: Owen, Handbook of Statistical Tables, Table A–4 “Chi-Square Distribution Table,” © 1962 by
Addison-Wesley Publishing Company, Inc. Copyright renewal © 1990. Reproduced by permission of
Pearson Education, Inc.
Area ␣
␹2


blu38582_IFC.qxd

9/13/10

Table E

7:09 PM

Page 1

The Standard Normal Distribution

Cumulative Standard Normal Distribution
z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

Ϫ3.4

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0003

.0002

Ϫ3.3

.0005

.0005

.0005

.0004

.0004

.0004

.0004

.0004

.0004

.0003

Ϫ3.2

.0007

.0007

.0006

.0006

.0006

.0006

.0006

.0005

.0005

.0005

Ϫ3.1

.0010

.0009

.0009

.0009

.0008

.0008

.0008

.0008

.0007

.0007

Ϫ3.0

.0013

.0013

.0013

.0012

.0012

.0011

.0011

.0011

.0010

.0010

Ϫ2.9

.0019

.0018

.0018

.0017

.0016

.0016

.0015

.0015

.0014

.0014

Ϫ2.8

.0026

.0025

.0024

.0023

.0023

.0022

.0021

.0021

.0020

.0019

Ϫ2.7

.0035

.0034

.0033

.0032

.0031

.0030

.0029

.0028

.0027

.0026

Ϫ2.6

.0047

.0045

.0044

.0043

.0041

.0040

.0039

.0038

.0037

.0036

Ϫ2.5

.0062

.0060

.0059

.0057

.0055

.0054

.0052

.0051

.0049

.0048

Ϫ2.4

.0082

.0080

.0078

.0075

.0073

.0071

.0069

.0068

.0066

.0064

Ϫ2.3

.0107

.0104

.0102

.0099

.0096

.0094

.0091

.0089

.0087

.0084

Ϫ2.2

.0139

.0136

.0132

.0129

.0125

.0122

.0119

.0116

.0113

.0110

Ϫ2.1

.0179

.0174

.0170

.0166

.0162

.0158

.0154

.0150

.0146

.0143

Ϫ2.0

.0228

.0222

.0217

.0212

.0207

.0202

.0197

.0192

.0188

.0183

Ϫ1.9

.0287

.0281

.0274

.0268

.0262

.0256

.0250

.0244

.0239

.0233

Ϫ1.8

.0359

.0351

.0344

.0336

.0329

.0322

.0314

.0307

.0301

.0294

Ϫ1.7

.0446

.0436

.0427

.0418

.0409

.0401

.0392

.0384

.0375

.0367

Ϫ1.6

.0548

.0537

.0526

.0516

.0505

.0495

.0485

.0475

.0465

.0455

Ϫ1.5

.0668

.0655

.0643

.0630

.0618

.0606

.0594

.0582

.0571

.0559

Ϫ1.4

.0808

.0793

.0778

.0764

.0749

.0735

.0721

.0708

.0694

.0681

Ϫ1.3

.0968

.0951

.0934

.0918

.0901

.0885

.0869

.0853

.0838

.0823

Ϫ1.2

.1151

.1131

.1112

.1093

.1075

.1056

.1038

.1020

.1003

.0985

Ϫ1.1

.1357

.1335

.1314

.1292

.1271

.1251

.1230

.1210

.1190

.1170

Ϫ1.0

.1587

.1562

.1539

.1515

.1492

.1469

.1446

.1423

.1401

.1379

Ϫ0.9

.1841

.1814

.1788

.1762

.1736

.1711

.1685

.1660

.1635

.1611

Ϫ0.8

.2119

.2090

.2061

.2033

.2005

.1977

.1949

.1922

.1894

.1867

Ϫ0.7

.2420

.2389

.2358

.2327

.2296

.2266

.2236

.2206

.2177

.2148

Ϫ0.6

.2743

.2709

.2676

.2643

.2611

.2578

.2546

.2514

.2483

.2451

Ϫ0.5

.3085

.3050

.3015

.2981

.2946

.2912

.2877

.2843

.2810

.2776

Ϫ0.4

.3446

.3409

.3372

.3336

.3300

.3264

.3228

.3192

.3156

.3121

Ϫ0.3

.3821

.3783

.3745

.3707

.3669

.3632

.3594

.3557

.3520

.3483

Ϫ0.2

.4207

.4168

.4129

.4090

.4052

.4013

.3974

.3936

.3897

.3859

Ϫ0.1

.4602

.4562

.4522

.4483

.4443

.4404

.4364

.4325

.4286

.4247

Ϫ0.0

.5000

.4960

.4920

.4880

.4840

.4801

.4761

.4721

.4681

.4641

For z values less than Ϫ3.49, use 0.0001.
Area

z

0


blu38582_IFC.qxd

9/13/10

Table E

7:09 PM

Page 2

(continued )

Cumulative Standard Normal Distribution
z

.00

.01

.02

.03

.04

.05

.06

.07

.08

.09

0.0

.5000

.5040

.5080

.5120

.5160

.5199

.5239

.5279

.5319

.5359

0.1

.5398

.5438

.5478

.5517

.5557

.5596

.5636

.5675

.5714

.5753

0.2

.5793

.5832

.5871

.5910

.5948

.5987

.6026

.6064

.6103

.6141

0.3

.6179

.6217

.6255

.6293

.6331

.6368

.6406

.6443

.6480

.6517

0.4

.6554

.6591

.6628

.6664

.6700

.6736

.6772

.6808

.6844

.6879

0.5

.6915

.6950

.6985

.7019

.7054

.7088

.7123

.7157

.7190

.7224

0.6

.7257

.7291

.7324

.7357

.7389

.7422

.7454

.7486

.7517

.7549

0.7

.7580

.7611

.7642

.7673

.7704

.7734

.7764

.7794

.7823

.7852

0.8

.7881

.7910

.7939

.7967

.7995

.8023

.8051

.8078

.8106

.8133

0.9

.8159

.8186

.8212

.8238

.8264

.8289

.8315

.8340

.8365

.8389

1.0

.8413

.8438

.8461

.8485

.8508

.8531

.8554

.8577

.8599

.8621

1.1

.8643

.8665

.8686

.8708

.8729

.8749

.8770

.8790

.8810

.8830

1.2

.8849

.8869

.8888

.8907

.8925

.8944

.8962

.8980

.8997

.9015

1.3

.9032

.9049

.9066

.9082

.9099

.9115

.9131

.9147

.9162

.9177

1.4

.9192

.9207

.9222

.9236

.9251

.9265

.9279

.9292

.9306

.9319

1.5

.9332

.9345

.9357

.9370

.9382

.9394

.9406

.9418

.9429

.9441

1.6

.9452

.9463

.9474

.9484

.9495

.9505

.9515

.9525

.9535

.9545

1.7

.9554

.9564

.9573

.9582

.9591

.9599

.9608

.9616

.9625

.9633

1.8

.9641

.9649

.9656

.9664

.9671

.9678

.9686

.9693

.9699

.9706

1.9

.9713

.9719

.9726

.9732

.9738

.9744

.9750

.9756

.9761

.9767

2.0

.9772

.9778

.9783

.9788

.9793

.9798

.9803

.9808

.9812

.9817

2.1

.9821

.9826

.9830

.9834

.9838

.9842

.9846

.9850

.9854

.9857

2.2

.9861

.9864

.9868

.9871

.9875

.9878

.9881

.9884

.9887

.9890

2.3

.9893

.9896

.9898

.9901

.9904

.9906

.9909

.9911

.9913

.9916

2.4

.9918

.9920

.9922

.9925

.9927

.9929

.9931

.9932

.9934

.9936

2.5

.9938

.9940

.9941

.9943

.9945

.9946

.9948

.9949

.9951

.9952

2.6

.9953

.9955

.9956

.9957

.9959

.9960

.9961

.9962

.9963

.9964

2.7

.9965

.9966

.9967

.9968

.9969

.9970

.9971

.9972

.9973

.9974

2.8

.9974

.9975

.9976

.9977

.9977

.9978

.9979

.9979

.9980

.9981

2.9

.9981

.9982

.9982

.9983

.9984

.9984

.9985

.9985

.9986

.9986

3.0

.9987

.9987

.9987

.9988

.9988

.9989

.9989

.9989

.9990

.9990

3.1

.9990

.9991

.9991

.9991

.9992

.9992

.9992

.9992

.9993

.9993

3.2

.9993

.9993

.9994

.9994

.9994

.9994

.9994

.9995

.9995

.9995

3.3

.9995

.9995

.9995

.9996

.9996

.9996

.9996

.9996

.9996

.9997

3.4

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9997

.9998

For z values greater than 3.49, use 0.9999.
Area

0

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Page i

E I G H T H

E D I T I O N

Elementary
Statistics
A Step by Step Approach

Allan G. Bluman
Professor Emeritus
Community College of Allegheny County

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Page ii

TM

ELEMENTARY STATISTICS: A STEP BY STEP APPROACH, EIGHTH EDITION
Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas,
New York, NY 10020. Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Previous
editions © 2009, 2007, and 2004. No part of this publication may be reproduced or distributed in any form or by
any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill
Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or
broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the
United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 0 QDB/QDB 1 0 9 8 7 6 5 4 3 2 1
ISBN 978–0–07–338610–2
MHID 0–07–338610–3

ISBN 978–0–07–743858–6 (Annotated Instructor’s Edition)
MHID 0–07–743858–2
Vice President, Editor-in-Chief: Marty Lange
Vice President, EDP: Kimberly Meriwether David
Senior Director of Development: Kristine Tibbetts
Editorial Director: Stewart K. Mattson
Sponsoring Editor: John R. Osgood
Developmental Editor: Adam Fischer
Marketing Manager: Kevin M. Ernzen
Senior Project Manager: Vicki Krug
Senior Buyer: Sandy Ludovissy
Designer: Tara McDermott
Cover Designer: Ellen Pettengell
Cover Image: © Ric Ergenbright/CORBIS
Senior Photo Research Coordinator: Lori Hancock
Compositor: MPS Limited, a Macmillan Company
Typeface: 10.5/12 Times Roman
Printer: Quad/Graphics
All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Library of Congress Cataloging-in-Publication Data
Bluman, Allan G.
Elementary statistics : a step by step approach / Allan Bluman. — 8th ed.
p. cm.
Includes bibliographical references and index.
ISBN 978–0–07–338610–2 — ISBN 0–07–338610–3 (hard copy : alk. paper) 1. Statistics—Textbooks.
I. Title.
QA276.12.B59 2012
519.5—dc22
2010031466

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Page iii

About the Author
Allan G. Bluman
Allan G. Bluman is a professor emeritus at the Community College of Allegheny County,
South Campus, near Pittsburgh, Pennsylvania. He has taught mathematics and statistics
for over 35 years. He received an Apple for the Teacher award in recognition of his bringing excellence to the learning environment at South Campus. He has also taught statistics for Penn State University at the Greater Allegheny (McKeesport) Campus and at the
Monroeville Center. He received his master’s and doctor’s degrees from the University
of Pittsburgh.
He is also author of Elementary Statistics: A Brief Version and co-author of Math in Our
World. In addition, he is the author of four mathematics books in the McGraw-Hill
DeMystified Series. They are Pre-Algebra, Math Word Problems, Business Math, and
Probability.
He is married and has two sons and a granddaughter.
Dedication: To Betty Bluman, Earl McPeek, and Dr. G. Bradley Seager, Jr.

iii


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Page iv

statistics
Hosted by ALEKS Corp.

Connect Statistics Hosted by ALEKS Corporation is an exciting, new assignment and
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Built by Statistics Educators
for Statistics Educators
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Page vi

statistics
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Page vii

Built by Statistics Educators
for Statistics Educators
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Page viii

Contents
Preface xii

CHAPTE R

2–2

The Histogram 51

1

The Frequency Polygon 53
The Ogive 54

The Nature of Probability
and Statistics 1

Relative Frequency Graphs 56
Distribution Shapes 59

Introduction 2

1–1
1–2
1–3

Descriptive and Inferential
Statistics 3
Variables and Types of Data 6
Data Collection and Sampling Techniques 9

2–3

Observational and Experimental Studies 13
Uses and Misuses of Statistics 16
Suspect Samples 17
Ambiguous Averages 17
Changing the Subject 17
Detached Statistics 18
Implied Connections 18
Misleading Graphs 18
Faulty Survey Questions 18

1–6

Pareto Charts 70
The Time Series Graph 71
The Pie Graph 73
Misleading Graphs 76
Stem and Leaf Plots 80
Summary 94

CHAPTE R

Introduction 104

3–1

Frequency Distributions
and Graphs 35
2–1

Measures of Central
Tendency 105
The Mean 106
The Median 109
The Mode 111
The Midrange 114

Summary 25

2

3

Data Description 103

Computers and Calculators 19

CHAPTE R

Other Types of Graphs 68
Bar Graphs 69

Random Sampling 10
Systematic Sampling 11
Stratified Sampling 12
Cluster Sampling 12
Other Sampling Methods 12

1–4
1–5

Histograms, Frequency Polygons,
and Ogives 51

The Weighted Mean 115
Distribution Shapes 117

3–2

Measures of Variation 123
Range 124

Population Variance and Standard Deviation 125

Introduction 36

Sample Variance and Standard Deviation 128

Organizing Data 37

Variance and Standard Deviation
for Grouped Data 129

Categorical Frequency Distributions 38
Grouped Frequency Distributions 39

Coefficient of Variation 132

All examples and exercises in this textbook (unless cited) are hypothetical and are presented to enable students to achieve a basic understanding of the statistical concepts explained. These examples and exercises should not be used in lieu of medical, psychological, or other professional advice. Neither the author nor
the publisher shall be held responsible for any misuse of the information presented in this textbook.

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Page ix

Contents

Range Rule of Thumb 133
Chebyshev’s Theorem 134
The Empirical (Normal) Rule 136

3–3

Measures of Position 142
Standard Scores 142
Percentiles 143
Quartiles and Deciles 149
Outliers 151

3–4

Mean 259
Variance and Standard Deviation 262
Expectation 264

5–3
5–4

The Binomial Distribution 270
Other Types of Distributions
(Optional) 283
The Multinomial Distribution 283
The Poisson Distribution 284
The Hypergeometric Distribution 286
Summary 292

Exploratory Data Analysis 162
The Five-Number Summary and Boxplots 162
Summary 171

CHAPTE R
CHAPTE R

4

Probability and Counting
Rules 181

The Normal Distribution 299
Introduction 300

6–1

Introduction 182

4–1

4–2
4–3

The Addition Rules for
Probability 199
The Multiplication Rules and Conditional
Probability 211
The Multiplication Rules 211

Conditional Probability 216
Probabilities for “At Least” 218

4–4

4–5

6–2

6–3

CHAPTE R

6–4

CHAPTE R

5–2

Probability
Distributions 253
Mean, Variance, Standard Deviation,
and Expectation 259

7

Confidence Intervals
and Sample Size 355
Introduction 356

7–1

Confidence Intervals for
the Mean When s Is
Known 357
Confidence Intervals 358
Sample Size 363

7–2

Introduction 252

5–1

The Normal Approximation to the Binomial
Distribution 340
Summary 347

5

Discrete Probability
Distributions 251

The Central Limit Theorem 331
Distribution of Sample Means 331
Finite Population Correction
Factor (Optional) 337

Probability and Counting Rules 237
Summary 242

Applications of the Normal
Distribution 316
Finding Data Values Given Specific
Probabilities 319
Determining Normality 322

Counting Rules 224
The Fundamental Counting Rule 224
Factorial Notation 227
Permutations 227
Combinations 229

Normal Distributions 302
The Standard Normal
Distribution 304
Finding Areas Under the Standard Normal
Distribution Curve 305
A Normal Distribution Curve as a Probability
Distribution Curve 307

Sample Spaces and
Probability 183
Basic Concepts 183
Classical Probability 186
Complementary Events 189
Empirical Probability 191
Law of Large Numbers 193
Subjective Probability 194
Probability and Risk Taking 194

6

7–3

Confidence Intervals for the Mean
When s Is Unknown 370
Confidence Intervals and Sample Size
for Proportions 377
Confidence Intervals 378
Sample Size for Proportions 379

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Page x

Contents

x

7–4

Confidence Intervals for Variances

and Standard Deviations 385
Summary 392

CHAPTE R

8

Hypothesis Testing 399
Introduction 400

8–1

8–2

Steps in Hypothesis
Testing—Traditional
Method 401
z Test for a Mean 413
P-Value Method for Hypothesis Testing 418

8–3
8–4
8–5
8–6

t Test for a Mean 427
z Test for a Proportion 437
x2 Test for a Variance or Standard Deviation 445
Additional Topics Regarding Hypothesis
Testing 457

Confidence Intervals and Hypothesis Testing 457

10–2 Regression 551
Line of Best Fit 551
Determination of the Regression
Line Equation 552

10–3 Coefficient of Determination
and Standard Error of the
Estimate 565
Types of Variation for the Regression
Model 565
Residual Plots 568
Coefficient of Determination 569
Standard Error of the Estimate 570
Prediction Interval 572

10–4 Multiple Regression (Optional) 575
The Multiple Regression Equation 577
Testing the Significance of R 579
Adjusted R 2 579
Summary 584

Type II Error and the Power of a Test 459
Summary 462
CHAPTE R

9

Testing the Difference

Between Two Means, Two
Proportions, and
Two Variances 471
Introduction 472

9–1
9–2

9–3
9–4
9–5

Testing the Difference Between
Two Means: Using the z Test 473
Testing the Difference Between Two
Means of Independent Samples:
Using the t Test 484
Testing the Difference Between Two Means:
Dependent Samples 492
Testing the Difference Between Proportions 504
Testing the Difference Between
Two Variances 513
Summary 524
Hypothesis-Testing Summary 1 532

CHAPTE R

10

Correlation and

Regression 533
Introduction 534

10–1 Scatter Plots and
Correlation 535
Correlation 538

CHAPTE R

11

Other Chi-Square Tests 591
Introduction 592

11–1 Test for Goodness
of Fit 593
Test of Normality
(Optional) 598

11–2 Tests Using Contingency
Tables 606
Test for Independence 606
Test for Homogeneity of Proportions 611
Summary 621

CHAPTE R

12

Analysis of Variance 629

Introduction 630

12–1 One-Way Analysis of
Variance 631
12–2 The Scheffé Test
and the Tukey Test 642
Scheffé Test 642
Tukey Test 644

12–3 Two-Way Analysis of
Variance 647
Summary 661
Hypothesis-Testing
Summary 2 669


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Page xi

Contents

xi

APPENDIX

A

Algebra Review 753

APPENDIX

B–1

Writing the Research
Report 759

APPENDIX

B–2

Bayes’ Theorem 761

APPENDIX

B–3

Alternate Approach to
the Standard Normal
Distribution 765

The Wilcoxon Rank Sum Test 683
The Wilcoxon Signed-Rank Test 688
The Kruskal-Wallis Test 693
The Spearman Rank Correlation Coefficient
and the Runs Test 700

APPENDIX

C

Tables 769

APPENDIX

D

Data Bank 799

Rank Correlation Coefficient 700

APPENDIX

E

Glossary 807

APPENDIX

F

Bibliography 815

APPENDIX

G

Photo Credits 817

APPENDIX

H

Selected Answers SA–1
Instructor’s Edition replaces
Appendix H with all answers
and additional material for
instructors.

CHAPTE R

13

Nonparametric
Statistics 671
Introduction 672

13–1 Advantages and
Disadvantages of
Nonparametric Methods 673
Advantages 673
Disadvantages 673
Ranking 673

13–2 The Sign Test 675
Single-Sample Sign Test 675

Paired-Sample Sign Test 677

13–3
13–4
13–5
13–6

The Runs Test 702
Summary 710
Hypothesis-Testing Summary 3 716
CHAPTE R

14

Sampling and
Simulation 719
Introduction 720

14–1 Common Sampling
Techniques 721
Random Sampling 721
Systematic Sampling 725
Stratified Sampling 726
Cluster Sampling 728
Other Types of Sampling Techniques 729

14–2 Surveys and Questionnaire Design 736
14–3 Simulation Techniques and the Monte Carlo
Method 739
The Monte Carlo Method 739

Summary 745

Index

I–1


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Page xii

Preface
Approach

Elementary Statistics: A Step by Step Approach was written as an aid in the beginning
statistics course to students whose mathematical background is limited to basic algebra.
The book follows a nontheoretical approach without formal proofs, explaining concepts
intuitively and supporting them with abundant examples. The applications span a broad
range of topics certain to appeal to the interests of students of diverse backgrounds
and include problems in business, sports, health, architecture, education, entertainment,
political science, psychology, history, criminal justice, the environment, transportation,
physical sciences, demographics, eating habits, and travel and leisure.

About This
Book

While a number of important changes have been made in the eighth edition, the learning
system remains untouched and provides students with a useful framework in which to
learn and apply concepts. Some of the retained features include the following:
• Over 1800 exercises are located at the end of major sections within each chapter.
• Hypothesis-Testing Summaries are found at the end of Chapter 9 (z, t, x2, and
F tests for testing means, proportions, and variances), Chapter 12 (correlation,
chi-square, and ANOVA), and Chapter 13 (nonparametric tests) to show students
the different types of hypotheses and the types of tests to use.
• A Data Bank listing various attributes (educational level, cholesterol level, gender,
etc.) for 100 people and several additional data sets using real data are included
and referenced in various exercises and projects throughout the book.
• An updated reference card containing the formulas and the z, t, x2, and PPMC
tables is included with this textbook.
• End-of-chapter Summaries, Important Terms, and Important Formulas give
students a concise summary of the chapter topics and provide a good source for
quiz or test preparation.
• Review Exercises are found at the end of each chapter.
• Special sections called Data Analysis require students to work with a data set to
perform various statistical tests or procedures and then summarize the results. The
data are included in the Data Bank in Appendix D and can be downloaded from
the book’s website at www.mhhe.com/bluman.
• Chapter Quizzes, found at the end of each chapter, include multiple-choice,
true/false, and completion questions along with exercises to test students’
knowledge and comprehension of chapter content.
• The Appendixes provide students with an essential algebra review, an outline for
report writing, Bayes’ theorem, extensive reference tables, a glossary, and answers
to all quiz questions, all odd-numbered exercises, selected even-numbered
exercises, and an alternate method for using the standard normal distribution.
• The Applying the Concepts feature is included in all sections and gives students
an opportunity to think about the new concepts and apply them to hypothetical

examples and scenarios similar to those found in newspapers, magazines, and radio
and television news programs.

xii


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Page xiii

Preface

Changes in
the Eighth
Edition

xiii

Overall
• Added over 30 new Examples and 250 new Exercises throughout the book.
• Chapter summaries were revised into bulleted paragraphs representing each section
from the chapter.
• New Historical Notes and Interesting facts have been added throughout the book.
Chapter 1
Updated and added new Speaking of Statistics. Revised the definition of nominal level
of measurement.

Chapter 6
Revised presentation for finding areas under the standard normal distribution curve. New
figures created to clarify explanations for steps in the Central Limit Theorem.
Chapter 7
Changed section 7.1 to Confidence Intervals for the Mean When s is Known. Maximum
error of the estimate has been updated to the margin of error. Updated the Formula for the
Confidence Interval of the Mean for a Specific a to include when s is Known. Added
assumptions for Finding a Confidence Interval for a Mean When s is Known. Revised
the explanation for rounding up when determining sample size. Added assumptions for
Finding a Confidence Interval for a Mean when s is Unknown. Added assumptions for
Finding a Confidence Interval for a Population Proportion. Added assumptions for Finding
a Confidence Interval for a Variance or Standard Deviation.
Chapter 8
Added assumptions for the z Test for a Mean When s Is Known. Added assumptions for
the t Test for a Mean When s Is Unknown. Added assumptions for Testing a Proportion.
Chapter 9
Revised the assumptions for the z Test to Determine the Difference Between Two Means.
Added that it will be assumed that variances are not equal when using a t test to test
the difference between means when the two samples are independent and when the
samples are taken from two normally or approximately normally distributed populations.
Added assumptions for the t Test for Two Independent Means When s1 and s2
Are Unknown. Added assumptions for the t Test for Two Means When the Samples Are
Dependent. Added assumptions for the z Test for Two Proportions. Revised the assumptions for Testing the Difference Between Two Variables.
Chapter 10
Added assumptions for the Correlation Coefficient. Residuals, are now covered in full
with figures illustrating different examples of Residual Plots.