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113
3.4 Exploratory Data Analysis
e. Show the box plots for the two groups. Did men or women have the most variation in
finish times? Explain.
SELF test
41. Annual sales, in millions of dollars, for 21 pharmaceutical companies follow.
8408
1374
1872
8879
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
434
Chapter 10
Inference About Means and Proportions with Two Populations
Applications
A BusinessWeek/Harris survey asked senior executives at large corporations their opinions
about the economic outlook for the future. One question was, Do you think that
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
Supplementary Exercises
393
WEB file
FirstBirth
Supplem
entary
Exercise
s
A production
line
operates
with a
mean
filling
weight
of
16
ounces
per
containe
r.
Overfilling or
underfill
ing
presents
a
serious
problem
and
when
detected
requires
the
operator
to
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
108
Chapter 3
Descriptive Statistics: Numerical Measures
What percentage of students have an SAT verbal score greater than 615?
What percentage of students have an SAT verbal score greater than 715?
What percentage of students have an SAT verbal score bet
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
468
Chapter 11
Inferences About Population Variances
Compute the sample mean.
Compute the sample standard deviation.
Compute a 95% confidence interval for the population standard deviation.
Part variability is critical in the manufacturing of ball bearing
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
387
9.8 Determining the Sample Size for a Hypothesis Test About a Population Mean
A production line operation is tested for filling weight accuracy using the following
hypotheses.
Hypothesis
Conclusion and Action
H0:
16
Filling okay; keep running
Ha :
1
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
520
Chapter 13
Experimental Design and Analysis of Variance
Thus, the individual 95% confidence interval for method A goes from 62 5.19
56.81 to 62 5.19 67.19. Because the sample sizes are equal for the Chemitech
experiment, the individual confidence inte
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
540
Chapter 13
Experimental Design and Analysis of Variance
Step 1. Compute the total sum of squares.
a
SST(xijk
b
r
x )2
(13.27)
i 1j 1k 1
Step
2.
Compute the sum of squares for factor A.
a
SSA br (xi. x )2
(13.28)
i 1
Step
3.
Compute the sum of squares
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
528
Chapter 13
Experimental Design and Analysis of Variance
making a Type I error for the overall experiment to be EW, we simply use a
comparisonwise error rate equal to EW/C. In the Chemitech experiment, if we want
to use Fishers LSD procedure to test a
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
562
The
statistical
methods
used in
studying the
relationship
between two
variables
were first
employed by
Sir Francis
Galton
(18221911).
Galton was
interested in
studying the
relationship
between a
fathers
height and
the sons
height.
Galtons
disciple,
Ka
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
554
Chapter 13
Experimental Design and Analysis of Variance
Use analysis of variance to test for any significant differences due to years of experience.
Use a .05 level of significance, and for now, ignore the effect of position.
At the .05 level of signi
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
605
14.8 Residual Analysis: Validating Model Assumptions
Develop the estimated regression equation that could be used to predict the price given
the weight.
Test for the significance of the relationship at the .05 level of significance.
Did the estimated
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
542
Chapter 13
FIGURE 13.6
Experimental Design and Analysis of Variance
MINITAB OUTPUT FOR THE GMAT TWOFACTOR DESIGN
SOURCE
DF
SS
MS
F
P
Factor A
2
6100
3050
1.38
0.299
Factor B
2
45300
22650
10.27
0.005
Interaction
4
11200
2800
1.27
0.350
Error
9
19850
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
526
Chapter 13
Experimental Design and Analysis of Variance
Many practitioners find it easier to determine how large the difference
between the sample means must be to reject H0. In this case the test statistic is xi
xj, and the test is conducted by the f
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
591
14.5 Testing for Significance
FIGURE 14.7 EXAMPLE OF A LINEAR APPROXIMATION OF A NONLINEAR
RELATIONSHIP
y
Actual
relationship
^
y = b0 + b1x
x
Smallest
Largest
x value
x value
Range of x
values observed
linear approximation provided by y b0 b1x is goo
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
Appendix 13.3 Analysis of a Completely Randomized Design Using StatTools
FIGURE 13.8 EXCEL SOLUTION FOR THE AIR TRAFFIC CONTROLLER STRESS TEST
A
B
C
D
1
Controller
System A
2
1
15
15
18
3
2
14
14
14
4
3
10
11
15
5
4
13
12
17
6
5
16
13
16
7
6
13
13
13
E
F
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
CHAPTER 13
Experimental Design
and Analysis of Variance
Estimates: The F Test
CONTENTS
STATISTICS IN PRACTICE: BURKE
MARKETING SERVICES, INC.
AN INTRODUCTION TO
EXPERIMENTAL DESIGN AND
ANALYSIS OF VARIANCE
Data Collection Assumptions
for Analysis of
Varia
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
593
14.5 Testing for Significance
Does the t test indicate a significant relationship between grade point average and
monthly salary? What is your conclusion? Use .05.
Test for a significant relationship using the F test. What is your conclusion? Use .05.
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
539
13.5 Factorial Experiment
TABLE 13.11 ANOVA TABLE
FOR THE TWOFACTOR FACTORIAL
EXPERIMENT WITH r REPLICATIONS
Source
Sum
Degrees
Mean
of Freedom
Square
of Variation of Squares
Factor A
SSA
Factor B
SSB
SSA
a 1
MSA
a 1
SSB
Interaction
SSAB
Error
SSE
To
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
522
Chapter 13
Experimental Design and Analysis of Variance
Compute the sum of squares due to error.
Compute the mean square due to error.
Set up the ANOVA table for this problem.
At the .05 level of significance, test whether the means for the three trea
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
504
Chapter 12
Tests of Goodness of Fit and Independence
FIGURE 12.4 EXCEL WORKSHEET FOR THE SCOTT MARKETING RESEARCH
GOODNESS OF FIT TEST
A
B
C
D
E
1 Goodness of Fit Test
2
3
Observed
Expected
4
Frequency Frequency
Calculations
5
48
60
=(A5B5)^2/B5
6
98
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STATISTIC 101

Fall 2015
577
14.3 Coefficient of Determination
TABLE 14.4 COMPUTATION OF THE TOTAL SUM OF SQUARES FOR ARMANDS
PIZZA PARLORS
xiStudent
yiQuarterly
Restaurant
Population
Sales
i
(1000s)
($1000s)
Squared
Deviation
y
y
Deviation
(
y y)2
i
i
1
2
58
72
5,184
2
6
105
25
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
529
13.3 Multiple Comparison Procedures
Use analysis of variance to test for a significant difference among the means of the three
treatments.
Use Fishers LSD procedure to determine which means are different.
Applications
15. To test whether the mean time
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
13.1 An Introduction to Experimental Design and Analysis of Variance
509
FIGURE 13.1 COMPLETELY RANDOMIZED DESIGN FOR EVALUATING
THE CHEMITECH ASSEMBLY METHOD EXPERIMENT
Employees at the plant in
Columbia, South Carolina
Random sample of 15 employees
is s
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
Statistics in Practice
507
cereals and stated what they thought about
the taste of each.
STATISTICS in PRACTICE
BURKE MARKETING SERVICES,
INC.*
CINCINNATI, OHIO
Burke Marketing Services, Inc., is one of the
most experienced market research firms in
the i
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
534
Chapter 13
TABLE 13.8
Experimental Design and Analysis of Variance
ANOVA TABLE FOR THE AIR TRAFFIC CONTROLLER STRESS TEST
Source
of Variation
Sum
Degrees
Mean
of Squares
of Freedom
Square
Treatments
21
2
10.5
Blocks
30
5
6.0
Error
19
10
1.9
Total
70
1
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
581
14.3 Coefficient of Determination
16. The data from exercise 2 follow.
xi
3
12
6
20 14
yi
55
40
55
10 15
The estimated regression equation for these data is y 68
3x.
Compute SSE, SST, and SSR.
Compute the coefficient of determination r2. Comment on th
National School of Statistics andInformation Analysis
STATISTIC 101

Fall 2015
549
Supplementary Exercises
Use .05 to test for any significant difference in the mean expense ratio among the four
types of stock funds.
The U.S. Census Bureau computes quarterly vacancy and homeownership rates by state and
metropolitan statistical area.