ES9 Additional Exercises
Chapter 1
1.
Determine which of the following statements is descriptive in nature and which is
inferential.
a.
99% of all big and tall travelers dislike cramped airline seating the most.
b.
99% of the 10,000 King-Size Co. customers dislike cramped airline seating the most.
2.
The Design, Sample, and Method section of an article titled "Making Behavior Changes
After a Myocardial Infarction" (Western Journal of Nursing Research, Aug. 1993) discusses the
selection of 16 informants who constituted 8 family dyads. The article states that, "to initiate
contact with informants, names of persons who met the criteria were obtained from the medical
records of a cardiac rehabilitation center in central Texas. Potential informants were then
contacted by telephone to obtain preliminary consent. Confidentiality and anonymity of
informants were ensured by coding the data to identify informants and link dyads."
a.
Is this a judgment sample or a probability sample?
b.
Is it appropriate to perform statistical inference using this sample? Justify your answer.
3.
The August 29/September 5, 1994 issue of U.S. News & World Report references a study
by health economists at the University of Southern California that indicated that Alzheimer's
disease cost the nation $82.7 billion a year in medical expenses and lost productivity. Patients'
earning loss was $22 billion, the value of time of unpaid caregivers was $35 billion, and the cost
of paid care was $24 billion.
a.
What is the population?
b.
What is the response variable?
c.
What is the parameter?
d.
What is the statistic?
4.
A USA Snapshot from USA Today (Nov. 1, 1994) described the greatest sources of
stress in starting a company. According to the snapshot, the CEOs of Inc. magazine's 500
fastest-growing private companies gave the following responses: 50% said company finances,
23% said the need to succeed, 10% said time commitments, 9% said personal relationships,
and 8% were classified as "other." Would the data collected and used to determine these
percentages be classified as qualitative or quantitative?
5.
The June 1994 issue of Good Housekeeping reported on a study on rape. The study
found that women who screamed, bit, kicked, or ran were more likely to avoid rape than women
who tried pleading, crying, or offered no resistance, and they were no more apt to be injured.
The authors, however, cautioned that the study could not be interpreted as proof that all women
should forcefully resist. The study involved 150 Omaha, Nebraska, police reports of rape or
attempted rape.
a.
Are the data in this study attribute or numerical?
b.
Is this a judgment or a probability sample?
Chapter 2
1. The USA Snapshot ® "How to say I love you" reports the results of a David Michaelson &
Associates survey for Ethel M Chocolates, on the best way to show affection.
Best way to show affection Give gift Hold hands Hugging/kissing
Smiling Other
Percent who said
10%
10%
51%
20%
9%
Draw a Pareto diagram picturing this information.
2. The January 10, 1991, USA Snapshot ® "What's in U.S. landfills" reports the percentages
for each type of waste in our landfills: food-4%, glass-2%, metal-14%, paper-38%, plastic-18%,
yard waste-11%, other-13%.
a. Construct a Pareto diagram displaying this information.
b. Because of the size of the "other" category, the Pareto diagram may not be the best graph
to use. Explain why, and describe what additional information is needed to make the Pareto
diagram more appropriate.
3. The closing prices (nearest dollar) of the first 50 common stocks listed in the New York
Stock Exchange with a value between $10 and $99 on July 23, 1998 was as follows:
30
26
13
75
52
26
72
24
37
90
41
26
31
36
57
11
58
17
35
22
28
16
52
12
21
47
65
12
75
28
35
13
17
38
25
17
22
31
32
52
19
45
11
14
27
17
48
52
54
43
Source: USA Today, July 23, 1998. p. 5B.
a. Construct a stem-and-leaf plot of these data.
b. Use the plot to determine the lowest and the highest stock price from those selected.
c. What price interval defined by the plot contains the most values?
4. In the May 1990 issue of the journal Social Work, the following ungrouped frequency
distribution was used to represent the "size of families":
Number of Children
Number of MexicanLiving at Home
American Women
0
23
1
22
2
17
3
7
4
1
Source: copyright 1990, National Association of Social Workers, Inc. Social Work
a. Which column represents the "size" of families? the "frequency" of those sizes?
b. Construct a frequency histogram of this distribution.
(Retain these answers for use in Exercise 2.21.)
5. All of the third-graders at Roth Elementary School were given a physical-fitness strength
test. These data resulted:
12
22
6
9
2
9
5
9
3
5
16
1
22
18
6
12
21
23
9
10
24
21
17
11
18
19
17
5
14
16
19
19
18
3
4
21
16
20
15
14
17
4
5
22
12
15
18
20
8
10
13
20
6
9
2
17
15
9
4
15
14
19
3
24
a. Construct a dotplot.
b. Prepare a grouped frequency distribution using classes 1-4, 4-7, and so on, and draw a
histogram of the distribution.
c. Prepare a grouped frequency distribution using classes 0-3, 3-6, 6-9, and so on, and draw a
histogram of the distribution.
d. Prepare a grouped frequency distribution using class boundaries -2.5, 2.5, 7.5, 12.5 and so
on, and draw a histogram of the distribution.
e. Prepare a grouped frequency distribution using classes of your choice, and draw a
histogram of the distribution.
f. Describe the shape of the histogram found in (b), (c), (d), and (e) separately. Relate the
distribution seen in the histogram to the distribution seen in the dotplot.
g. Discuss how the number of classes used and the choice of class boundaries used affect the
appearance of the resulting histogram.
6. The following 40 amounts are the fees that Fast Delivery charged for delivering small freight
items last Thursday afternoon.
4.03 3.56 3.10 6.04 5.62 3.16 2.93 3.82 4.30 3.86
4.57 3.59 4.57 5.16 2.88 5.02 5.46 3.87 6.81 4.91
3.62 3.62 3.80 3.70 4.15 4.07 3.77 5.77 7.86 4.63
4.81 2.86 5.02 5.24 4.02 5.44 4.65 3.89 4.00 2.99
a. Classify these data into a grouped frequency distribution.
b. Construct a relative frequency histogram of these data.
7. An article titled "Financing Your Kids' College Education" (Farming, Sept./Oct. 1994) listed
the following in-state tuition and fees per school year for 14 land-grant universities: 1554, 2291,
2084, 4443, 2884, 2478, 3087, 3708, 2510, 2055, 3000, 2052, 2550, 2013.
a. Find the mean in-state tuition and fees per school year.
b. Find the median in-state tuition and fees per school year.
c. Find the midrange in-state tuition and fees per school year.
c. Find the mode, if one exists, per school year.
8. Atlantic Monthly (Nov. 1990) contains an article titled "The Case for More School Days." The
number of days in the standard school year is given for several different countries as follows:
Country
n(days)/yr
Country
n(days)/year
Japan
243
New Zealand
190
West Germany
226-240
Nigeria
190
South Korea
220
British Columbia
185
Israel
216
France
185
Luxembourg
216
Ontario
185
Soviet Union
211
Ireland
184
Netherlands
200
New Brunswick
182
Scotland
200
Quebec
180
Thailand
200
Spain
180
Hong Kong
195
Sweden
180
England/Wales
192
United States
180
Hungary
192
French Belgium
175
Swaziland
191
Flemish Belgium
160
Finland
190
a. Find the mean and median number of days per year of school for the countries listed. (Use
the midpoint of the 226-240 interval for West Germany when computing your answers.)
b. Construct a stem-and-leaf display of these data.
c. Describe the relationship between the mean and the median and what properties of the data
cause the mean to be larger than the median.
(Retain solution for use in answering Exercise 2.12.)
9. USA Today, July 22, 1998, reported the following statistics about the average in-season
daily greens fees by state at US golf courses.
Highest: Hawaii, $85.70
Lowest: South Dakota, $23.80
a. Based on this information, find the "average" of the 50 state average fees.
b. Explain why your answer in part (a) is the only average value you can determine from the
given information.
c. If you were told the mean value of the 50 state averages is $37.30, what can you tell about
their distribution.
10. USA Today, 10-28-94, reported on the average annual pay received by all workers
covered by state and federal unemployment insurance for the 50 states. Connecticut had the
highest with $33,169, South Dakota had the lowest with $18,613.
a. Estimate the national average with the midrange for the states.
b. The national average was reported to be $26,362. What can you conclude about the
distribution of the state averages based on the relationship between the midrange and the
national average?
11. An article titled "Financing Your Kids' College Education" (Farming, Sept./Oct. 1994) listed
the following in-state tuition and fees per school year for 14 land-grant universities: 1554, 2291,
2084, 4443, 2884, 2478, 3087, 3708, 2510, 2055, 3000, 2052, 2550, 2013. Find the following:
a. variance s²
b. standard deviation s
12 a. Find the range and the standard deviation for the number of days per year of school,
using the data in Exercise 2.8.
b. Draw lines on the stem-and-leaf diagram drawn in answering Exercise 2.8 that represent the
range and the standard deviation. Remember, the standard deviation is a measure for the
mean.
c. Describe the relationship among the distribution of the data, the range, and the standard
deviation.
13. A 1993 issue of Library Journal (Vol. 118, No. 17) gives the following table for the salaries
of minority placements by type of library.
Library Type Number Average Salary
Academic
46
$27,825
Public
34
24,657
School
23
30,336
Special
16
29,406
Other
4
25,200
a. Find the total of all salaries for the above 123 individuals.
b. Find the mean salary for the above 123 individuals.
c. What is the modal library type? Explain.
d. Find the standard deviation for the above 123 salaries.
14. A research study of manual dexterity involved determining the time required to complete a
task. The time required for each of 40 disabled individuals is as follows (data are ranked):
7.1
7.2
7.2
7.6
7.6
7.9
8.1
8.1
8.1
8.3
8.3
8.4
8.4
8.9
9.0
9.0
9.1
9.1
9.1
9.1
9.4
9.6
9.9
10.1 10.1 10.1 10.2 10.3 10.5 10.7
11.0 11.1 11.2 11.2 11.2 12.0 13.6 14.7 14.9 15.5
Find:
a. Q1
b. Q2
c. Q3
d. P95
e. the 5-number summary
f. Draw the box-and-whisker display.
15.
Consider the following set of ignition times that were recorded for a synthetic fabric.
30.1 30.1 30.2 30.5 31.0 31.1 31.2 31.3 31.3 31.4
31.5 31.6 31.6 32.0 32.4 32.5 33.0 33.0 33.0 33.5
34.0 34.5 34.5 35.0 35.0 35.6 36.0 36.5 36.9 37.0
37.5 37.5 37.6 38.0 39.5
Find:
a. the median
b. the midrange
c. the midquartile
d. the 5-number summary
e. Draw the box-and-whisker display.
16. In a study involving mastery learning (Research in Higher Education, Vol. 20, No. 4,
1984), 34 students took a pretest. The mean score was 11.04, and the standard deviation was
2.36. Find the z-score for scores of 9 and 15 on the 20-question pretest.
17. An article titled "Computer-Enhanced Algebra Resources: The Effects on Achievement
and Attitudes" (International Journal of Math Education in Science and Technology, 1980, Vol.
11, No. 4) compared algebra courses that used computer-assisted instruction with courses that
do not. The scores that the computer-assisted instruction group made on an achievement test
consisting of 50 problems had these summary statistics: n = 57, x = 23.14, s = 7.02.
a. Find the limits within which at least 75% of the scores fell.
b. If the scores are normally distributed, what percentage of the scores will be below 30.16?
18. Below is a sample of one-way commute times, to the nearest minute, for 50 college
students who are gainfully employed.
2
10
3
5
1
19
14
3
15
12
30
10
2
8
19
17
12
29
21
29
15
23
3
24
4
16
49
15
64
5
3
22
19
1
48
4
25
7
22
4
3
10
33
12
14
30
10
13
5
23
a. Construct three different kinds of graphs for this data.
b. Find the five measures of central tendency.
c. Find the three measures of dispersion.
d. Using one graph from part (a), one measure of central tendency from part (b) and one
measure of dispersion from part (c), write a short presentation of the 50 data that you
believe best describes the typical employed college student's commute to work.
e. Explain how the graph and the two statistics used in answering part (d) best describe the
situation.
19. Compute the mean and the standard deviation for the following set of data. Then find the
percentage of the data that is within two standard deviations of the mean.
1 | .4 .7 .1
2 | .4 .5
3 | .5 .0 .4 .1
4 | .4
5 | .5 .8 .7
6 | .8 .8 .2 .8 .6
7 | .5
8 |
9 | .4
20. Ask one of your instructors for a list of exam grades (15 to 25 grades) from a class.
a. Find five measures of central tendency.
b. Find the three measures of dispersion.
c. Construct a stem-and-leaf display. Does this diagram suggest that the grades are normally
distributed?
d. Find the following measures of location: (1) Q1 and Q3, (2) P15 and P60, (3) the standard
score z for the highest grade.
21. In the May 1990 issue of the journal Social Work, Marlow reports the following results:
Number of Children
MexicanAngloLiving at Home
American Women
American Women
0
23
38
1
22
9
2
17
15
3
7
9
4
1
1
Copyright 1990, National Association of Social Workers, Inc. Social Work.
a. Construct a frequency histogram for each of the preceding distributions. Draw them on the
same axis, using two different colors, so that you can compare their distributions. (See
Exercise 2.4.)
b. Calculate the mean and standard deviation for the Mexican-American data.
c. Calculate the mean and standard deviation for the Anglo-American data.
d. Do these two distributions seem to be different? Cite specific reasons for your answer.
22. Mutual funds attract millions of private investors every year. USA Today assembles a
Mutual Fund Scoreboard that lists 15 of the largest stock funds available and a Mutual Fund
Spotlight that shows the 14 top yielding growth and income funds during the past four weeks.
Three more funds were selected randomly from the general listing of all mutual funds. Midway
through 1998, the combined lists are shown below, together with each fund’s total return for the
year:
Fund Name
Fidelity Magellan
Vanguard Index 500 Port
Washington Mutual Inv
Investment Co of America
Fidelity Growth & Income
Fidelity Contrafund
Vanguard Windsor II
Amer Cent/20th C Ultra
Vanguard Wellington
Fidelity Puritan
Fidelity Equity-Inc
Fidelity Adv Growth Oppty
Vanguard Windsor
Income Fund of America
Janus Fund
Pioneer Capital Growth
Total Return (%)
22.0
20.9
14.6
15.7
19.5
23.0
16.2
30.4
9.7
13.0
12.9
14.5
10.1
6.9
26.2
8.0
Fund Name
Berkshire Cap Gro & Value
Marsico Growth & Income
Nations Mars Gro & Inc
Strong Blue Chip 100 Fund
Janus Growth & Income
Excelsior Inst Value Equity
Schroder Large Cap Equity
Strong Total Return Fund
Reynolds Blue Chip Growth
Diversified Investors
Strong Growth & Income
Newpoint Equity Fund
New Providence Cap Gro
Weitz Partners Value Fund
Putnam High Yield
Standish Internat’l Equity
Total Return (%)
41.1
39.3
39.2
30.9
29.8
22.3
26.7
24.6
35.1
30.1
26.9
23.6
10.9
30.2
4.6
30.1
Source: USA Today, July 23, 1998, pp. 3B,6B.
a. Omit names and build a 4 x 8 table of ranked total return percentages in ascending order,
reading vertically in each column.
b. Construct a 5-number summary table.
c. Find the midquartile total return percentage and the interquartile range.
d. What are the z-scores for Berkshire Capital Growth & Value, Income Fund of America, and
Janus Fund?
e. Based on the data and your calculations, can you pinpoint the three funds selected at
random?
Chapter 3
1. In a study involving children's fear related to being hospitalized, the age and the score each
child made on the Child Medical Fear Scale (CMFS) were:
Age (x)
8
9
9
10
11
9
9
9
11
11
CMFS score (y)
31
25
40
27
35
29
25
34
27
36
Construct a scatter diagram of these data. (Retain for use in answering Exercise 3.4.)
2. Walter Payton was one of the NFL's greatest running backs. Below are listed the number of
carries and the total yards gained in each of his 13 years with the Chicago Bears.
Number Carries 196 311 339 333 369 317 339 148 314 381 324 321 146
Total Yards
679 1390 1852 1359 1610 1460 1222 596 1421 1684 1551 1333 586
a. Construct a scatter diagram depicting these data.
b. How would you describe this scatter diagram? What do you see that is unusual about the
scatter diagram?
c. What circumstances might explain this "two group" appearance of the data points? Explain.
3. Total solar eclipses actually take place nearly as often as total lunar eclipses, but they are
visible over a much narrower path. Both the path width and the duration vary substantially from
one eclipse to the next. The table below shows the duration (seconds) and path width (miles) of
44 total solar eclipses measured in the past and those projected to the year 2010:
Date
1950
1952
1954
1955
1956
1958
1959
1961
1962
1963
1965
1966
1968
1970
1972
1973
1974
1976
1977
1979
1980
1981
Duration (s)
73
189
155
427
284
310
181
165
248
99
315
117
39
207
155
423
308
286
157
169
248
122
Width (mi)
83
85
95
157
266
129
75
160
91
63
123
52
64
95
109
159
214
123
61
185
92
67
Date
1983
1984
1985
1986
1987
1988
1990
1991
1992
1994
1995
1997
1998
1999
2001
2002
2003
2005
2006
2008
2009
2010
Duration (s)
310
119
118
1
7
216
152
413
320
263
129
170
248
142
296
124
117
42
247
147
399
320
Width (mi)
123
53
430
1
3
104
125
160
182
117
48
221
94
69
125
54
338
17
114
144
160
160
Source: The World Almanac and Book of Facts 1998, p. 296.
a. Draw a scatter diagram showing duration, y, and path width, x, for the total solar eclipses.
b. How would you describe this diagram?
4. In an article titled "Self-Reported Fears of Hospitalized School-Age Children" (Journal of
Pediatric Nursing, Vol. 9, No. 2, 1994), the authors report a correlation of 0.10 between the ages
of children and the score they made on the Child Medical Fear Scale (CMFS). Suppose the
ages and CMFS scores for ten children were as follows (same data as Exercise 3.1):
CMFS Score 31
25
40
27
35
29
25
34
27
36
Age
8
9
9
10
11
9
9
9
11
11
Find: a. SS(x)
b. SS(y)
c. SS(xy)
d. the value of r for these data
5. Consider the following data, which give the weight (in thousands of pounds) x and gasoline
mileage (miles per gallon) y for ten different automobiles.
x
2.5
3.0
4.0
3.5
2.7
4.5
3.8
2.9
5.0
2.2
y
40
43
30
35
42
19
32
39
15
44
Find: a. SS(x)
b. SS(y)
c. SS(xy)
d. Pearson's product moment r
6. An article titled "Leader Power, Commitment Satisfaction, and Propensity to Leave a Job
Among U.S. Accountants" (Journal of Social Psychology, Vol. 133, No. 5, Oct. 1993) reported a
linear correlation coefficient of -0.61 between satisfaction with work scores and propensity to
leave a job scores. Suppose similar assessments of work satisfaction, x, and propensity to
leave a job, y, gave the following scores.
x
12
24
17
28
24
36
20
y
44
36
25
23
32
17
24
a. Find the linear correlation between x and y.
b. What does the value of this correlation coefficient seem to be telling us? Explain.
7. Cable television video networks can be measured on the basis of both their number of
noncable affiliates and number of subscribers. Below is a table of 18 video networks, their
affiliates and subscribers (in millions):
Network
ESPN-1
CNN
TNT
TBS
C-SPAN
USA Network
TNN
LIFETIME Television
The Family Channel
Arts & Entertainment
MTV: Music Television
Nickelodian
Nick at Nite
The Weather Channel
Headline News
CNBC
QVC Network
VH-1
Affiliates
27,600
11,528
10,538
11,668
6,003
12,500
17,636
8,300
13,352
12,000
9,176
11,788
11,711
6,500
6,470
11,711
5,895
6,088
Subscribers
71.1
71.0
70.5
69.9
69.7
69.7
68.9
67.0
66.9
66.9
66.7
66.0
66.0
64.2
64.0
60.0
58.2
56.3
Source: Cable Television Developments, National Cable Television Assn., Jan.-Mar. 1997.
a. Draw a scatter diagram of the two variables, affiliates and subscribers.
b. Find the linear correlation coefficient and interpret the results.
8. An article titled "College Recreation Facility Survey" (Athletic Business, April 1994) reported
the following results from 358 four-year colleges and universities in the United States and
Canada.
Total Square Feet Devoted
Enrollment
Number of Schools
to Recreation per School
0 - 1,249
58
47,864
1,250 - 2,499
53
71,828
2,500 - 4,999
53
89,716
5,000 - 9,999
62
101,016
10,000 - 17,999
68
127,952
18,000 or over
64
200,896
a. Using the midpoint of the first five enrollment classes and 25,000 in place of the class
18,000 or over for the x-values and the total square feet devoted to recreation per school for
the y-values, find the linear correlation coefficient between x and y.
b. What does the value of this correlation seem to be telling us? Explain.
9. An article titled "Microbioluminometry Assay (MBA): Determination of Erythromycin Activity
in Plasma or Serum" (Journal of Pharmaceutical sciences, Dec. 1989) compares the MBA
assay with another method, agar diffusion plate assay, for determining the erythromycin activity
in plasma or serum. The MBA technique is economical because it requires less sample and
reagents.
If X represents the agar diffusion plate assay in micrograms per milliliter and Y represents the
MBA assay in micrograms per milliliter, then the results may be expressed as
Y = 0.054128 + 0.92012X
r = 0.9525
n = 206
If the agar diffusion plate assay determined the level of erythromycin to be 1.200, predict what
the MBA assay would be.
10. In the article "Beyond Prediction: The Challenge of Minority Achievement in Higher
Education" (Lunneborg and Lunneborg, Journal of Multicultural Counseling and Development),
the relationship between high school GPA and first-year university GPA was investigated for the
following groups: Asian Americans, blacks, chicanos, Native Americans, and whites. For the 43
Native Americans, the correlation was found to be 0.26 and the equation of the line of best fit
was found to be university GPA = 1.85 + 0.30  high school GPA. Both GPAs were 4.0 scales.
Use the equation of the line of best fit to predict the mean first-year-university GPA for all Native
Americans who had a high school GPA equal to 3.0.
11. People not only live longer today but also live longer independently. The May/June 1989
issue of Public Health Reports published an article titled "A Multistate Analysis of Active Life
Expectancy." Two of the variables studied were a person's current age and the expected
number of years remaining.
Age x
65
67
69
71
73
75
77
79
81
83
Years Remaining y 16.5 15.1 13.7 12.4 11.2 10.1 9.0
8.4
7.1
6.4
a. Draw a scatter diagram.
b. Calculate the equation of best fit.
c. Draw the line of best fit on the scatter diagram.
d. What is the expected years remaining for a person who is 70 years old? Find the answer in
two different ways: Use the equation from (b) and use the line on the scatter diagram from
(c).
e. Are you surprised that the data all lie so close to the line of best fit? Explain why the ordered
pairs follow the line of best fit so closely.
12. A record of maintenance costs is kept for each of several cash registers throughout a
department store chain. A sample of 14 registers gave the following data:
a.
b.
c.
d.
13.
a.
b.
c.
d.
Age x
Maintenance Cost y
|
Age x
Maintenance Cost y
(years)
(dollars)
|
(years)
(dollars)
6
142
|
2
99
7
231
|
1
114
1
73
|
9
191
3
90
|
3
160
6
176
|
8
155
4
132
|
9
231
5
167
|
8
202
Draw a scatter diagram that shows these data.
Calculate the equation of the line of best fit.
A particular cash register is eight years old. How much maintenance (cost) do you predict it
will require this year?
Interpret your answer to (c).
The following data are the ages and the asking prices for 19 used foreign compact cars:
Age x
Price y
|
Age x
Price y
(years)
(x $100)
|
(years)
(x $100)
3
68
|
6
42
5
52
|
8
22
3
63
|
5
50
6
24
|
6
36
4
60
|
5
46
4
60
|
7
36
6
28
|
4
48
7
36
|
7
20
2
68
|
5
36
2
64
|
Draw a scatter diagram.
Calculate the equation of the line of best fit.
Graph the line of best fit on the scatter diagram.
Predict the average asking price for all such foreign cars that are five years old. Obtain this
answer in two ways: Use the equation from (b) and use the line drawn in (c).
14. An article titled "Women, Work and Well-Being: The Importance of Work Conditions
(Health and Social Behavior, Vol. 35, No. 3, Sept. 1994) studied 202 full-time homemakers and
197 employed wives. The linear correlation coefficient between family income and education
was reported to equal 0.43 for the participants in the study. A similar study involving eight
individuals gave the following results. (x represents the years of education, and y represents the
family income in thousands of dollars).
x
12
13
10
14
11
14
16
16
y
34
45
36
47
43
35
50
42
a. Find the linear correlation between x and y.
b. Find the equation of the line of best fit.
15. You have probably thought about the number of hours you spend at work or at leisure, but
have you ever wondered about the relationship between the number of hours that all Americans
spend per week at work and at leisure?
Year
Work
Leisure
1995
50.6
19.2
1993
50.0
19.0
1989
48.7
16.6
1984
47.3
16.6
1980
46.9
19.2
1975
43.1
24.3
USA Today December 26, 1996
a. How many hours did you, personally, spend working last week? How many hours did you
spend at leisure pursuits?
b. Construct one graph using years as a horizontal axis, hours as the vertical axis and plot
hours of work and hours of leisure using two different colored dots. Connect the dots.
c. Do you see any pattern(s) to the graph? Explain.
d. Is there a relationship between the two variables, hours spent at work and hours devoted to
leisure? When people spend more time at one, do they spend less time at the other? Use
the techniques learned in this chapter to present graphic and numerical statistics that aid in
the explanation of your answer to these questions.
16. "Fast-Food Fat Counts Full of Surprises," in USA Today, 10-20-94, compared some of the
popular fast-food items in calories and fat.
Calories (x) 270
420
210
450
130
310
290
450
446
640
233
Fat (y)
9
20
10
22
6
25
7
20
20
38
11
a.
b.
c.
d.
x
552
360
838
199
360
y
55
6
20
12
36
Draw a scatter diagram of these data.
Calculate the linear coefficient, r.
Find the equation of the line of best fit.
Explain the meaning of the above answers.
345
28
552
22
17. A biological study of a minnow called the blacknose dace was conducted. The length, y, in
millimeters and the age, x, to the nearest year were recorded.
x
0
3
2
2
1
3
2
4
1
1
y
25
80
45
40
36
75
50
95
30
15
a. Draw a scatter diagram of these data.
b. Calculate the correlation coefficient.
c. Find the equation of the line of best fit.
d. Explain the meaning of the above answers.
18. Investors in mutual funds keep a sharp eye on the total return on their money. They also
are aware of the risk involved in their investment, commonly measured by a fund’s volatility (the
greater the volatility, the higher the risk). Below is a list of 30 mutual funds randomly selected in
1998 from Fortune’s list of stock and bond funds, together with their 5-year total return (%) and
risk assessment:
Fund Name
MFS Emerging Growth
Kaufmann
AIM Constellation A
Weitz Hickory
Oak Value
Gabelli Westwood Equity
Nationwide
Fidelity Growth/Income
Stratton Growth
GAM International A
Scudder International
Janus Worldwide
Oppenheimer Global A
New Perspective
Putnam Europe Growth A
Total Return
21.5
19.7
17.6
29.9
25.6
23.0
24.3
22.6
21.3
22.6
14.3
23.6
19.0
18.8
22.7
Risk
20.6
18.4
18.4
19.7
13.0
12.3
12.0
13.0
11.8
19.9
13.7
13.7
14.4
12.1
14.6
Fund Name
AIM Balanced A
Greenspring
Delaware A
Calamos Convertible A
Managers Bond
Harbor Bond
Northeast Investors
Strong Gov’t. Securities
Lexington GNMA Income
Marshall Gov’t. Income
Wright U.S. Treasury
Excelsior Tax-Exempt
Vanguard Municipal
Goldman Sachs Global
Capital World Bond
Total Return
15.9
14.0
13.6
14.3
10.3
7.3
13.6
7.0
6.9
5.8
6.3
7.6
6.5
7.2
5.9
Risk
10.8
7.2
8.6
9.9
5.4
4.4
5.5
4.4
3.5
3.7
7.5
6.7
5.5
4.1
4.9
Source: Fortune, “The Best Mutual Funds”, August 17, 1998, pp. 88-98.
a. Draw a scatter diagram with 5-year total return as the y-axis and risk as the x-axis.
b. Calculate the correlation coefficient.
c. Would you conclude that in order to obtain higher total returns, mutual fund investors must
take greater risks? Explain.
Chapter 4
1. An article titled "Pain and Pain-Related Side Effects in an ICU and on a Surgical Unit:
Nurses' Management" (American Journal of Critical Care, January 1994, Vol. 3, No. 1) gave the
following table summarizing the study participants. (Note: ICU is an acronym for intensive care
unit.)
Gender
ICU
Surgical Unit
Female
9
6
Male
11
18
One of these participants is randomly selected. Answer the following questions.
a. Are the events "being a female" and "being in the ICU" mutually exclusive?
b. Are the events "being in the ICU" and "being in the surgical unit" mutually exclusive?
c. Find P(ICU or female).
c. Find P(ICU or male).
2. Tracy Shark walked into the card room at her country club and played one hand of bridge at
one table and one hand of poker at another table. She was dealt a bridge hand with all 13 cards
in the same suit, and then she was dealt a poker hand with a royal flush. As she left the room
shaking her head, she was overheard mumbling, “I doubt that will happen again in a million
years.” Assuming the decks were shuffled and the dealers were straight, compute the
probability of the joint occurrence of the two events. Do you agree with Tracy?
3. The December 1994 issue of The American Spectator quotes a poll by the Times-Mirror
Center for the People and the Press as finding that 71% of Americans believe that the press
"gets in the way of society solving its problems."
a. If two Americans are randomly selected, find the probability that both will believe that the
press "gets in the way of society solving its problems."
b. If two Americans are selected, find the probability that neither of the two will believe that the
press "gets in the way of society solving its problems."
c. If three are selected, what is the probability that all three believe the press gets in the way?
4. The August 1, 1994, issue of The New Republic gives the results of a U.S. Justice
Department study which states that among white spousal murder victims, 62% are female. If the
records of three victims are randomly selected from a large data base of such murder victims,
what is the probability that all three victims are male?
5. An article involving smoking cessation intervention in Heart & Lung (March/April 1994, Vol.
23, No. 2) divided 80 subjects into a two-way classification:
Diagnosis
Group
Cardiovascular
Oncology
General Surgery
Experimental
10
14
13
Usual Care
12
16
15
Suppose one of these 80 subjects is selected at random. Find the probabilities of the following
events.
a. The subject is not in the experimental group.
b. The subject is in the experimental group and has oncology diagnosis.
c. The subject is in the experimental group or ha a cardiovascular diagnosis.
6. A study concerning coping strategies of abstainers from alcohol appeared in Image, the
Journal of Nursing Scholarship (Vol. 25, No. 1, Spring 1993). The study involved 23 subjects
who were classified according to sex as well as marital status as shown in the table.
Marital Status
Men
Women
Currently married
10
3
Divorced/separated
3
6
Never married
1
0
One of the subjects is selected at random. Find:
a. The probability the subject is currently married given that the individual is a man.
b. The probability the subject is a woman given that the individual is divorced/separated.
c. The probability the subject is a man given that the individual has never married.
7. An article titled "A Puzzling Plague" found in the January 14, 1991, issue of Time, stated
that one out of every ten American women will get breast cancer. It also states that of those who
do, one out of four will die of it. Use these probabilities to find the probability that a randomly
selected American woman will
a. never get breast cancer.
b. get breast cancer and not die of it.
c. get breast cancer and die from it.
8. The Pennsylvania Lottery game big 4 has been played for more than 18 years. The table
below lists the number of times each single-digit number was the winning number for each of
the four positions. The frequencies for each number in each position range from 304 to 367.
Number
0
1
2
3
4
5
6
7
8
9
First
343
326
347
320
304
321
339
348
337
360
Second
312
330
323
327
345
348
306
346
367
341
Third
352
351
315
350
331
322
329
351
329
315
Fourth
328
357
344
351
318
343
316
311
350
327
Total
1335
1364
1329
1348
1298
1334
1290
1356
1383
1343
a. Do the frequencies of each number as a winner in the first position appear to indicate that
the numbers occur randomly as first position winners? What statistical evidence can you
find to justify your answer? Present a convincing case.
b. Do the frequencies of each number as a winner in the second, third and fourth positions
appear to indicate that the numbers occur randomly as position winners? What statistical
evidence can you find to justify your answer? Present a convincing case.
c. Each single-digit number has appeared as a winning number a different number of times
ranging from 1290 to 1383. Do you think these numbers vary sufficiently to make a case
that the digits do not occur with equal probability? Present evidence to support your
answer.
9. According to the National Cancer Data Base report for Hodgkin's disease (CA-A Cancer
Journal for Clinicians, Jan./Feb. 1991), the highest percentage of patients (31%) were 20 to 29
years of age, and they had a three-year observed survival rate of 91%. What is the probability
that an individual who has been diagnosed with Hodgkin's disease is between 20 and 29 years
of age and will survive for three years?
Chapter 5
1. "How women define holiday shopping," a USA Snapshot® (12-9-94) reported that 50% said
"a pleasure," 22% said "a chore," 19% said "no big deal," and 8% said "a nightmare." The
percentages do not sum to 100% due to round-off error.
a. What is the variable involved, and what are the possible values?
b. Why is this variable not a random variable?
2. "Kids who smoke," a USA Snapshot (4-25-94), reports the percentage of children in each
age group who smoke.
Age, x
Percent Who Smoke
12
1.7
13
4.9
14
8.9
15
16.3
16
25.2
17
37.2
Is this a probability distribution? Explain why or why not.
3. A USA Snapshot® (11-1-94) titled "How many telephones we have" reported that 1% have
none, 11% have one, 31% have two, and 57% have three or more. Let x equal the number of
phones per home, and replace the category "three or more" with exactly "three."
a. Find the mean and standard deviation for the random variable x.
b. Explain the effect of replacing the category "three or more" with "three" had on the
distribution of x, the mean, and the standard deviation.
4. a. Use the probability distribution shown below and describe in your own words how the
mean of the variable x is found.
x
1
2
3
4
P(x) 0.1
0.2
0.3
0.4
b. Find the mean of x.
c. Find the deviation from the mean for each x-value.
d. Find the value of each "squared deviation from the mean."
e. Recalling your answer to (a), find the mean of the variable "squared deviation."
f. "Variance" was the name given to the "mean of the squared deviations." Explain how
formula (5.2) expresses the variance as a mean.
5. In California, 30% of the people have a certain blood type. What is the probability that
exactly 5 out of a randomly selected group of 14 Californians will have that blood type? (Find
the answer by using a table.)
6. On the average, 1 out of every 10 boards purchased by a cabinet manufacturer is unusable
for building cabinets. What is the probability that 8, 9, or 10 of a set of 11 such boards are
usable? (Find the answer by using a table.)
7. A local polling organization maintains that 90% of the eligible voters have never heard of
John Anderson, who was a presidential candidate in 1980. If this is so, what is the probability
that in a randomly selected sample of 12 eligible voters, 2 or fewer have heard of John
Anderson?
8. A basketball player has a history of making 80% of the foul shots taken during games. What
is the probability that he will miss three of the next five foul shots he takes?
9. According to an article in the February 1991 issue of Reader's Digest, Americans face a 1 in
20 chance of acquiring an infection while hospitalized. If the records of 15 randomly selected
hospitalized patients are examined, find the probability that
a. none of the 15 acquired an infection while hospitalized.
b. 1 or more of the 15 acquired an infection while hospitalized.
10. An article in the Omaha World-Herald (12-1-94) stated that only about 60% of the
individuals needing a bone marrow transplant find a suitable donor when they turn to registries
of unrelated donors. In a group of 10 individuals needing a bone marrow transplant,
a. what is the probability that all 10 will find a suitable donor among the registries of unrelated
donors?
b. what is the probability that exactly 8 will find a suitable donor among the registries of
unrelated donors?
c. what is the probability that at least 8 will find a suitable donor among the registries of
unrelated donors?
d. what is the probability that no more than 5 will find a suitable donor among the registries of
unrelated donors?
11. Colorado Rockies baseball player Larry Walker’s league-leading batting average reached
.344 after 415 times at bat during the 1998 season (ratio of hits to at bats). Suppose Walker has
five official times at bat during his next game. Assuming no extenuating circumstances and that
the binomial model will produce reasonable approximations, what is the probability that Walker:
a. gets less than two hits?
b. gets more than three hits?
c. goes five-for-five (all hits)?
12. According to Financial Executive (July/August 1993) disability causes 48% of all mortgage
foreclosures. Given that 20 mortgage foreclosures are audited by a large lending institution,
a. find the probability that 5 or fewer of the foreclosures are due to a disability.
b. find the probability that at least 3 are due to a disability.
13. Seventy-five percent of the foreign-made autos sold in the United States in 1984 are now
falling apart.
a. Determine the probability distribution of x, the number of these autos that are falling apart in
a random sample of five cars.
b. Draw a histogram of the distribution.
c. Calculate the mean and standard deviation of this distribution.
14. A 1998 survey conducted by Fortune revealed that the Marriott International workforce
was composed of 50.3% minorities. A further subdivision revealed 6.0% Asian, 24.2% black,
and 19.6% Hispanic.
Source: Fortune, “The Diversity Elite”, August 3, 1998, p. 114.
Find the mean and standard deviation of all samples of 25 randomly selected employees of the
Marriott International workforce for each of the three minority groups. Present your statistics in a
table.
15. A USA Snapshot® titled "Stress does not love company" (11-3-94) answered the question
"How people say they prefer to spend stressful times." Forty-eight percent responded "alone,"
29% responded "with family," 18% responded "with friends," and 5% responded "other/don't
know." Ten individuals are randomly selected and asked the question "How do you prefer to
spend stressful times?"
a. What is the probability that two or fewer will respond by saying "alone"?
b. Explain why this question can be answered using binomial probabilities.
16. For years, the manager of a certain company had sole responsibility for making decisions
with regards to company policy. This manager has a history of making the correct decision with
a probability of p. Recently company policy has changed, and now all decisions are to be made
by majority rule of a three-person committee.
a. Each member makes a decision independently, and each has a probability of p of making
the correct decision. What is the probability that the committee's majority decision will be
correct?
b. If p = 0.1, what is the probability that the committee makes the correct decision?
c. If p = 0.8, what is the probability that the committee makes the correct decision?
d. For what values of p is the committee more likely to make the correct decision by majority
rule than the former manager?
e. For what values (there are three) of p is the probability of a correct decision the same for the
manager and for the committee? Justify your answer.
17. Suppose one member of the committee in Exercise 5.16 always makes the decision by
rolling a die. If the die roll results in an even number, they vote for the proposal, and if an odd
number occurs, they vote against it. The other two members still decide independently and
have a probability of p of making the correct decision.
a. What is the probability that the committee's majority decision will be correct?
b. If p = 0.1, what is the probability that the committee makes the correct decision?
c. If p = 0.8, what is the probability that the committee makes the correct decision?
d. For what value of p is the committee more likely to make the correct decision by majority
rule than the former manager?
e. For what values of p is the probability of a correct decision the same for the manager and for
the committee? Justify your answer.
f. Why is the answer to (e) different than the answer to Exercise 5.16 (e)?
Chapter 6
1. According to the November 1993 issue of Harper's magazine, our kids spend from 1200 to
1800 hours a year in front of the television set. Suppose the time spent by kids in front of the
television set per year is normally distributed with a mean equal to 1500 hours and a standard
deviation equal to 100 hours.
a. What percentage spend between 1400 and 1600 hours?
b. What percentage spend between 1300 and 1700 hours?
c. What percentage spend between 1200 and 1800 hours?
c. Compare the results (a) through (c) with the empirical rule. Explain the relationship.
2. For a particular age group of adult males, the distribution of cholesterol readings, in mg/dl, is
normally distributed with a mean of 210 and a standard deviation of 15.
a. What percentage of this population would have readings exceeding 250?
b. What percentage would have readings less than 150?
3. At Pacific Freight Lines, bonuses are given to billing clerks when they complete 300 or more
freight bills during an eight-hour day. The number of bills completed per clerk per eight-hour
day is approximately normally distributed with a mean of 270 and a standard deviation of 16.
What proportion of the time should a randomly selected billing clerk expect to receive a bonus?
4. The waiting time x at a certain bank is approximately normally distributed with a mean of 3.7
min and a standard deviation of 1.4 min.
a. Find the probability that a randomly selected customer has to wait less than 2.0 min.
b. Find the probability that a randomly selected customer has to wait more than 6 min.
d. Find the value of the 75th percentile for x.
5. According to a USA Snapshot ® (10-26-94), the average annual salary for a worker in the
United States is $26,362. If we assume that the annual salaries for Americans are normally
distributed with a standard deviation equal to $6,500, find the following:
a. What percentage earn below $15,000?
b. What percentage earn above $40,000?
6. According to the 1991 issue of American Hospital Administration Hospital Statistics, the
average daily census total for 116 hospitals in Mississippi equals 10,872. Suppose the standard
deviation of the daily census totals for these hospitals equals 1505 patients. If the daily census
totals are normally distributed:
a. What percentage of the days does the daily census total less than 8500 patients in these
hospitals? Approximately how often should we expect this to occur?
b. What percentage of the days does the daily census total exceed 12,500 patients in these
hospitals? Approximately how often should we expect this to occur?
7.
A drug manufacturer states that only 5% of the patients using a particular drug will
experience side effects. Doctors at a large university hospital use the drug in treating 250
patients. What is the probability that 15 or fewer of the 250 patients experience side effects?
8. A survey in the March 1994 issue of Life magazine indicated that 9 out of 10 Americans pray
frequently and earnestly, and almost all say God has answered their prayers. Assuming "9 out
of 10" is accurate, use the normal approximation to the binomial to find the probability that in a
national survey of 1000 Americans, at least 925 will indicate that they pray frequently and
earnestly.
9. An article in Life magazine indicated than 60% of Americans have had a psychic
experience. An example of a psychic experience is dreaming about an event before it actually
occurs. Some experts call psychic experiences precognitions, whereas others write it off as pure
coincidence. Suppose a national survey of 2000 Americans is conducted and each is asked
whether or not they have had a psychic experience. Use the normal approximation to the
binomial distribution to find the probability that over 1,230 report such a phenomenon.
Source: Life, June, 1998. p. 89.
10. According to the Bureau of Justice Statistics Sourcebook of Criminal Justice Statistics
1992, 4.5% of young adults reported using alcohol daily for the past 30 days. Use the normal
approximation to the binomial distribution to find the probability that, in a national poll of 1024
young adults, between 35 and 50 inclusive will indicate that they have used alcohol daily for the
past 30 days.
a. Solve using normal approximation and Table 3.
b. Solve using a computer or calculator and the normal approximation method.
c. Solve using a computer or calculator and the binomial probability function.
11. An article in USA Today (4-4-91) quoted a study involving 3365 people in Minneapolis-St.
Paul between 1980 and 1982 and another 4545 between 1985 and 1987. It found that the
average cholesterol level for males was 200. The authors of the study say the results of their
study are probably similar nationwide. Assume that the cholesterol values for males in the
United States are normally distributed with a mean equal to 200 and a standard deviation equal
to 25.
a. What percentage have readings between 150 and 225?
b. What percentage have readings that exceed 250?
12. If 60% of the registered voters plan to vote for Ralph Brown for mayor of a large city. What
is the probability that less than half of the voters, in a poll of 200 registered voters, plan to vote
for Ralph brown?
Chapter 7
1. According to a USA Snapshot® (USA Today, October 21-23, 1994), the average amount
spent per month for long-distance calls through the long-distance carrier is $31.65. If the
standard deviation for long-distance calls through the long-distance carrier is $12.25 and a
sample of 150 customers is selected, the mean of this sample belongs to a sampling
distribution.
a. What is the shape of this distribution?
b. What is the mean of this sampling distribution?
c. What is the standard deviation of this sampling distribution?
2. More Americans heat their homes with natural gas than any other fuel. According to the
American Gas Association, the national average price of natural gas sold to residential
customers in 1997 was 62 cents per therm, about 18 percent less than it cost ten years earlier,
in inflation-adjusted dollars.
Source: 1997 Gas Facts, American Gas Association.
If the standard deviation for prices of natural gas sold to residential customers is 11 cents per
therm and a random sample of 200 residential customers in 1997 is selected, the mean of this
sample belongs to a sampling distribution.
a. What is the shape of this sampling distribution?
b. What is the mean of this sampling distribution?
c. What is the standard deviation of this sampling distribution?
3. According to the 1993 World Factbook, the 1993 total fertility rate (mean number of children
born per woman) for Madagascar is 6.75. Suppose the standard deviation of the total fertility
rate is 2.5. The mean number of children for a sample of 200 randomly selected women is one
value of many that form the sampling distribution of sample means.
a. What is the mean value for this sampling distribution?
b. What is the standard deviation of this sampling distribution?
c. Describe the shape of this sampling distribution.
4. According to the 1994 World Almanac, the average speed of winds in Honolulu, Hawaii,
equals 11.4 miles per hour. Assume that wind speeds are approximately normally distributed
with a standard deviation of 3.5 miles per hour.
a. Find the probability that the wind speed on any one reading will exceed 13.5 miles per hour.
b. Find the probability that the mean of a random sample of 9 readings exceeds 13.5 miles per
hour.
c. Do you think the assumption of normality is reasonable? Explain.
d. What effect do you think the assumption of normality had on the answers to (a) and (b)?
Explain.
5. According to the U.S. Dept. of Energy, the average price of unleaded regular gasoline sold
at service stations throughout the nation in 1996 was $1.23 per gallon. Assume that gasoline
prices in general are normally distributed with a standard deviation of $.16 per gallon.
Source: Energy Administration, U.S. Dept. of Energy, Monthly Energy Review, June 1997.
A random sample of 45 stations in 1996 is selected and the pump prices for unleaded regular
gasoline are recorded. Find the probability that the sample mean price:
a. exceeds $1.28 per gallon.
b. is less than $1.19 per gallon.
c. is between $1.20 and $1.27 per gallon.
6. According to the World Almanac and Book of Facts - 1994, the median weekly earnings of
full-time wage and salary women, age 16 years or older in 1992, equals $381. Assume that the
wages and salaries are normally distributed with  = $85.
a. Find the probability that the mean weekly earnings of a sample of 250 such women is
between $375 and $385, if the mean equals $381.
b. Do you think the assumption of normality is reasonable? Explain.
c. What effect do you think the assumption of normality about the x distribution had on the
answer to (a)? Explain.
d. Do you think the assumption of mean equals $381 is reasonable? Explain.
e. What effect do you think the assumption about the value of the mean had on the answer to
(a)? Explain.
7. According to the August 1994 issue of Employment and Earnings, the June 1994 average
weekly earnings for employees in general automotive repair shops was $406.15. Suppose the
standard deviation for the weekly earnings for such employees is $55.50. Assuming that this
mean and standard deviation are the current values, find the following probabilities for the mean
of a sample of 100 such employees.
a. The probability the mean of the sample is less than $400.
b. The probability the sample mean is between $400 and $410.
c. The probability the mean of the sample is greater than $415.
d. Explain why the assumption of normality about the x distribution was not involved in the
solution to (a), (b), and (c).
8. The Gallup Poll has been surveying the public for many years. When repeated sampling is
used to track America's attitudes, the sample statistic reported, the percentage of yes
responses, does not form a sampling distribution, but rather it forms a time series and
demonstrates a trend. (Time series is a topic not covered in this text; however, many of its
components are.) Complete the following questions to help recognize and understand the
difference between repeated samples that belong to a sampling distribution and those that
belong to a time series.
Year
1937
1949
1955
1967
1969
1971
1975
1978
1983
1984
1987
2000
Yes
34
48
52
57
54
66
73
76
80
78
82
xx
No
66
48
44
39
39
29
23
19
16
17
12
zz
a. Plot a scatter diagram displaying the Selected National Trend information (above), using the
year as the input variable and the percentage of yes responses as the output variable y.
b. On the scatter diagram drawn in (a), plot the percentages of the no responses as a second
output variable using the year number as the input variable x.
c. Do you see what could be called a trend? Explain.
d. Make a prediction for the percentage of Americans who would vote for a woman president.
How did you use the cases study information?
e. Sampling distributions involve repeated sampling from the same population, but with a
completely different purpose. Explain, in your own words, how a sampling distribution is
different than the chapter case study illustration.
f. Repeated sampling, like that in the chapter case study and that used in quality control, is
carried out for the purpose of "tracking" the statistic being studied. Describe, in your own
words, the purpose of studying a statistic from repeated samples as a sampling distribution.
9. According to an article in Pharmaceutical News (January 1991), a person age 65 or older
will spend, on the average, $300 on personal-care products per year. If we assume that the
amount spent on personal-care products by individuals 65 or older is normally distributed and
has a standard deviation equal to $75, what is the probability that the mean amount spent by 25
randomly selected such individuals will fall between $250 and $350?
10. A report in Newsweek (November 12, 1990) stated that the day-care cost per week in
Boston is $109. If this figure is taken as the mean cost per week and if the standard deviation
were known to be $20, find the probability that a sample of 50 day-care centers would show a
mean cost of $100 or less per week.
Chapter 8
1. An article titled "A Comparison of the Effects of Constant Co-operative Grouping versus
Variable Co-operative Grouping on Mathematics Achievement Among Seventh Grade
Students," (International Journal of Mathematics Education in Science and Technology, Vol.
24, No. 5, 1993) gives the mean percentile score on the California Achievement Test (CAT) for
20 students to be 55.20. Assume the population of CAT scores is normally distributed and that
 = 19.5.
a. Make a point estimate for the mean of the population the sample represents.
b. Find the maximum error of estimate for a level of confidence equal to 95%.
c. Construct a 95% confidence interval for the population mean.
d. Explain the meaning of each of the above answers.
2. According to a USA Snapshot® (USA Today, 11-3-94), the annual teaching income for ski
instructors in the Rocky Mountain and Sierra areas is $5600. (Assume  = $1000.)
a. If this figure is based on a survey of 15 instructors and if the annual incomes are normally
distributed, find a 90% confidence interval for , the mean annual teaching income for all ski
instructors in the Rocky Mountain and Sierra areas.
b. If the distribution of annual incomes is not normally distributed, what effect do you think that
would have on the interval answer in part (a)? Explain.
3. According to an article in Good Housekeeping (February 1991) a 128.lb woman who walks
for 30 minutes four times a week at a steady, 4 mi./hr pace can lose up to 10 pounds over a
span of a year. Suppose 50 women with weights between 125 and 130 lb performed the four
walks per week for a year and at the end of the year the average weight loss for the 50 was 9.1
lb. Assuming that the standard deviation, , is 5, complete the hypothesis test of Ho:  = 10.0
vs. Ha:   10.0 at the 0.05 level of significance using the p-value approach.
4. The gestation period (the elapsed time between conception and birth) of gray squirrels
measured in captivity is listed as 44 days as estimated by the author of Walker’s Mammals of
the World. It is recognized that the potential life span of animals is rarely attained in nature, but
the gestation period could be either shorter or longer.
Source: Walker’s Mammals of the World 5e, Johns Hopkins University Press, 1991.
Suppose the gestation period of a sample of 81 squirrels living in the wild is measured using the
latest techniques available, and the mean length of time is found to be 42.5 days. Test the
hypothesis that squirrels living in the wild have the same gestation period as those in captivity at
the 0.05 level of significance. Assume that  = 5 days. Use the classical approach.
a. Define the parameter.
b. State the null and alternative hypotheses.
c. Specify the hypothesis test criteria.
d. Present the sample evidence.
e. Find the probability distribution information. f. Determine the results.
5.
The USA Snapshot® “Holiday home trimmings” presented information about all American
households (page 626). One hundred fifty adult shoppers at a large shopping mall were asked
“How much (to the nearest $25) do you anticipate your family will spend on holiday decorations
this year?”
25 200 100 25 250
75 25 50 25 100
75 25 100 75 25
25 200 25
0 25
175 25 75 100 100
50 25 50 100 50
25
0
25
150
25
50
50
25
100
100
25
75
100
75
75
0
100
100
50
100
25
25
125
0
175
75
75
150
75
75
100
100
25
75
75
0
75
25
50
25
75
100
100
100
25
0
125
100
25
25
25
75
25
100
200
100
0
50
50
25
50
0
75
50
100
50
0
75
50
50
25
25
25
25
25
25
50
75
25
25
25
100
25
0
50
50
25
125
50
100
100
300
25
100
50
25
25
150
25
25
100
50
25
75
25
75
50
25
125
125
50
100
75
75
150
50
50
25
25
25
Use the above sample data to describe the anticipated amount households living near this mall
plan to spend on holiday decorations this year.
a. Describe the sample data using several numerical statistics and at least one graph.
b. Estimate the mean anticipated amount households living near this mall plan to spend on
holiday decorations this year. Use 95% level of confidence and assume  = 70.
c. Does the above sample suggest that the families who shop in this mall anticipate spending a
different average amount than all Americans according to “Holiday home trimmings”? Use
= 0.05.
d. Are the assumptions for the confidence interval and hypothesis test methods satisfied?
Explain.
Chapter 9
1. There seems to be no end to how large the signing bonuses professional athletes can
obtain when they start their careers. When the Indianapolis Colts gave Peyton Manning $11.6
million and the San Diego Chargers awarded Ryan Leaf $11.25 million as signing bonuses in
1998, both these amounts exceeded what the 1989 first round draft pick, Troy Aikman, earned
in his first five National Football League seasons combined while playing for the Dallas
Cowboys.
Source: Sports Illustrated, “Inside the NFL: Powerball Numbers”, August 10, 1998.
Suppose a sample of 18 new NFL players report their signing bonuses at the start of the 1998
season, and the results show a mean of $3.81 million and a standard deviation of $1.7 million.
a. Estimate with 95% confidence the mean signing bonus based on the report. [Specify the
population parameter of interest, the criteria, the sample evidence, and the interval limits.]
b. Discuss how this situation does or does not satisfy the assumptions for the inference.
2. Ten randomly selected shut-ins were each asked to list how many hours of television they
watched per week. The results are
82
66
90
84
75
88
80
94
110
91
Determine the 90% confidence interval estimate for the mean number of hours of television
watched per week by shut-ins. Assume the number of hours is normally distributed.
3. The weights of the drained fruit found in 21 randomly selected cans of peaches packed by
Sunny Fruit Cannery were (in ounces)
11.0 11.6 10.9 12.0 11.5 12.0 11.2 10.5 12.2 11.8 12.1
11.6 11.7 11.6 11.2 12.0 11.4 10.8 11.8 10.9 11.4
Using a computer or a calculator,
a. Calculate the sample mean and standard deviation.
b. Assume normality and construct the 98% confidence interval for the estimate of the mean
weight of drained peaches per can.
4. "Obesity raises heart-attack risk" according to a study published in the March 1990 issue of
the New England Journal of Medicine. "Those about 15 to 25 percent above desirable weight
had twice the heart disease rate." Suppose the data listed below are the percentages above
desired weight for a sample of patients involved in a similar study.
18.3 19.7 22.1 19.2 17.5 12.7 22.0 17.2 21.1 16.2 15.4
19.9 21.5 19.8 22.5 16.5 13.0 22.1 27.7 17.9 22.2 19.7
18.1 22.4 17.3 13.3 22.1 16.3 21.9 16.9 15.4 19.3
Use a computer or calculator to test the null hypothesis,  = 18%, versus the alternative
hypothesis,   18%. Use = 0.05.
5. A telephone survey was conducted to estimate the proportion of households with a personal
computer. Of the 350 households surveyed, 75 had a personal computer.
a. Give a point estimate for the proportion in the population who have a personal computer.
b. Give the maximum error of estimate with 95% confidence.
6.
An article titled "Why Don't Women Buy CDs?" appeared in the September 1994 issue of
Music magazine. Yehuda Shapiro, marketing director of Virgin Retail Europe, found that across
Europe 40% of his customers who buy classical records are women. Determine a 90%
confidence interval for the true value of p if the 40% estimate is based on 1000 randomly
selected buyers.
7. "Parents should spank children when they think it is necessary, said 51% of adult
respondents to a survey-though most child-development experts say spanking is not
appropriate. The survey of 7225 adults . . . was co-sponsored by Working Mother magazine and
Epcot Center at Walt Disney World." This statement appeared in the Rochester Democrat &
Chronicle (12-20-90). Find the 99% confidence maximum error of estimate for the parameter p,
P(should spank when necessary), for the adult population.
8. In a survey of 12,000 adults aged 19 to 74, National Cancer Institute researchers found that
9% in the survey ate at least the recommended two servings of fruit or juice and three servings
of vegetables per day (Ladies Home Journal, April 1991). Use this information to determine a
95% confidence interval for the true proportion in the population who follow the
recommendation.
9. a. Calculate the maximum error of estimate for p for the 95% confidence interval for each
of the situations listed in the table.
Approximate Value of p
Sample Size n
0.1
0.3
0.5
0.7
0.9
100
500
1000
1500
b. Explain the relationship between answers in columns 0.1 and 0.9; 0.3 and 0.7.
10. According to the June 1994 issue of Bicycling, only 16% of all bicyclists own helmets. You
wish to conduct a survey in your city to determine what percent of the bicyclists own helmets.
Use the national figure of 16% for your initial estimate of p.
a. Find the sample size if you want your estimate to be within 0.02 with 90% confidence.
b. Find the sample size if you want your estimate to be within 0.04 with 90% confidence.
c. Find the sample size if you want your estimate to be within 0.02 with 98% confidence.
d. What effect does changing the maximum error have on the sample size? Explain.
e. What effect does changing the level of confidence have on the sample size? Explain.
11. A bank believes that approximately 2/5 of its checking-account customers have used at
least one other service provided by the bank within the last six months. How large a sample will
be needed to estimate the true proportion to within 5% at the 98% level of confidence?
12.
Paul Polger, a meteorologist with the National Weather Service, says that weathermen
now accurately predict 82% of extreme weather events, up from 60% a decade ago. In fact,
Polger claims, “We’re doing as well in a two-day forecast as we did in a one-day forecast twenty
years ago.”
Source: Life, “Predicting: Yesterday, Today. and Tomorrow”, August, 1998.
You wish to conduct a study of extreme weather forecast accuracy by comparing local forecasts
with actual weather conditions occurring in your city.
a. What is the best estimate available for the probability of accuracy in predicting extreme
weather events.
b. Find the sample size if you want your estimate to be within 0.02 with 90% confidence.
c. Find the sample size if you want your estimate to be within 0.04 with 95% confidence.
d. Find the sample size if you want your estimate to be within 0.06 with 99% confidence.
e. If the level of confidence remains constant, what happens to the required sample size if you
wish to double the maximum error of your estimate?
13. According to the May 1990 issue of Good Housekeeping, only about 14% of lung cancer
patients survive for five years after diagnosis. Suppose you wanted to see if this survival rate
were still true. How large a sample would you need to take to estimate the true proportion
surviving for five years after diagnosis to within 1% with 95% confidence? (Use the 14% as the
value of p.)
14. The article "Making Up for Lost Time" (U.S. News & World Report, July 30, 1990) reported
that more than half of the country's workers aged 45 to 64 want to quit work before they reach
age 65. Suppose you conduct a survey of 1000 randomly chosen workers in order to test Ho: p
= 0.5 versus Ha: p < 0.5, where p represents the proportion who want to quit before they reach
age 65. 460 of the 1000 sampled want to quit work before age 65. Use = 0.01.
a. Calculate the value of the test statistic.
b. Solve using the p-value approach.
c. Solve using the classical approach.
15
Many students work full-time or part-time. Listed below is the amount earned last month by each
in a sample of 35 college students.
0
0
105
0
313
453
769
415
244
0
333
0
0
362
276
158
409
0
0
534
449
281
37
338
240
0
0
0
142
0
519
356
280
161
0
Use this sample data to describe the amount earned by working college students.
a. How many of the students in the sample above are working?
b. Describe the variable, amount earned by a working college student last month, using one
graph, one measure of central tendency, one measure of dispersion.
c. Find evidence to show that the assumptions for use of Student's t-distribution have been
satisfied.
d. Estimate the mean amount earned by a college student per month using a point estimate
and a 95% confidence interval.
e. A Statistical Snapshot® suggests the average amount earned each month by college
students is approximately $350. Does the sample show sufficient reason to reject that
claim?
16. Many U.S. housewives wouldn’t think of leaving home to go shopping without their stash
of coupons, as reported in a 1998 issue of Family Circle. In fact, couponing has been a popular
practice for over 30 years. The amount that people save at the supermarket by redeeming
coupons varies substantially; some shoppers routinely save $50 or more per trip, whereas
others save little if anything. Couponing has also been criticized for generating sales of frivolous
products and overstocking of items that ordinarily would have remained on the shelf, and it
takes longer to check out at the cash register. On the other hand, coupon queens tend to be
more educated and living in higher-income households.
Source: Family Circle, “The Great Grocery Challenge”, September 15, 1998.
Suppose the mean of all coupon sales at supermarkets in the U.S. is $10. A random sample of
25 shoppers with annual household incomes exceeding $75,000 is taken and reveals a mean
redemption of $15 and a standard deviation of $7. Do shoppers from the higher-income group
redeem coupons worth more than those redeemed by the rest of the nation? Use  = 0.01.
17. Home schooling became legal in all 50 states in 1993, thus allowing parents to take
charge of their kids’ education from kindergarten to college. Researchers estimate that as many
as 1.5 million children and teenagers in 1998 were being taught primarily by their mothers and
fathers; about five times as many as there were ten years earlier. This number is rather
remarkable considering that the number of two-income households also rose during the same
period. (i.e., Who’s staying at home teaching the kids?) The average ACT score for a homeschooled in 1998 was 23, whereas the average for traditionally schooled students was 21.
Source: Newsweek, “Learning at Home: Does it Pass the Test?”, October 5, 1998.
Suppose a recent survey of 22 home schoolers in your state revealed a mean ACT score of
23.2 and a standard deviation of 4.1. Do the ACT scores of home schoolers in your state
exceed the scores for the traditionally schooled? Use the 0.05 level of significance.
18. The LEXIS, a national law journal, found from a survey conducted on April 6-7, 1991, that
nearly two-thirds of the 800 people surveyed said doctors should not be prosecuted for helping
people with terminal illnesses commit suicide. The poll carries a margin of error of plus or minus
3.5%.
a. Describe how this survey of 800 people fits the properties of a binomial experiment.
Specifically identify: n, a trial, success, p, and x.
b. Exactly what is the "two-thirds" reported? How was it obtained? Is it a parameter or a
statistic?
c. Calculate the 95% confidence maximum error of estimate for the population proportion of all
people who believe doctors should not be prosecuted.
d. How is the maximum error, found in (c), related to the 3.5% mentioned in the survey report?
19. Prevention magazine reported in its latest survey that 64% of adult Americans, or 98
million people, were overweight. The telephone survey of 1254 randomly selected adults was
conducted November 8-29, 1990, and had a margin of error of three percentage points.
a. Calculate the maximum error of estimate for 0.95 confidence with p' = 0.64.
b. How is the margin of error of three percentage points related to answer (a)?
c. How large a sample would be needed to reduce the maximum error to 0.02 with 95%
confidence?
20.
"Two of five Americans believe the country should rely on nuclear power more than other
energy sources for energy in the 1990s, according to a poll released yesterday  .The
telephone poll, taken April 10 - 11, has a margin of error of plus or minus 3 points." This
statement appeared in the Rochester Democrat & Chronicle on April 21, 1991. Forty percent
plus or minus three points sounds like a confidence interval.
a. What is another name for the "margin of error of plus or minus 3 points"?
b. If we assume a 95% level of confidence, how large a sample is needed for a maximum error
of 0.03?
Chapter 10
1. When the Dow Jones industrial average dropped 512 points on August 31, 1998, it was the
largest point drop since the 554-point drop that hit the stock market on October 27, 1987. Prior
to that drop, some experts had predicted a 9,500 Dow before the end of the year, but after the
August slide, opinions changed. The consensus by many analysts seemed to be that the
market would not bounce back in time to even approach the level predicted by earlier estimates.
The bull was tired.
Source: Fortune, “Requiem for the Bull”,
September 28, 1998.
A random sample of 18 closing stock prices from the New York Stock Exchange was taken on
August 25, 1998 (about one week prior to the “crash”), and again using the same stocks on
September 15, 1998. Both dates are on a Tuesday. Results are shown in the table below:
Stock
1
2
3
4
5
6
7
8
9
August 25
10 ½
11 ¼
23 ¾
14
12 ½
19 ¾
27 ¼
32
56 ½
September 15
11
9
21 ¼
11 ½
7¼
18 ½
22 ½
24 ¼
59 ¼
Stock
10
11
12
13
14
15
16
17
18
August 25
7¾
14 ½
16 ¼
65 ½
53 ¼
43 ½
71
32 ½
17 ¼
September 15
8½
13 ½
17 ¼
63 ½
56 ¼
41 ½
70 ¼
34 ½
16 ½
a. On the basis of these data, construct a 90% confidence interval for the mean change from
August 25 to September 15.
b. Can you conclude that the stock market was still suffering from the August 31 slide by
September 15 or had it recovered? Explain.
2. An article titled, “Influencing Diet and Health Through Project LEAN” (Journal of Nutrition
Education, July/August 1994) compared 28 individuals with borderline-high or high cholesterol
levels before and after a nutrition education session. The participants’ cholesterol levels were
significantly lowered, and the p-value was reported to be less than 0.001. A similar study
involving 10 subjects was performed with the following cholesterol reading results:
Subject
1
2
3
4
5
6
7
8
9
10
Presession
295
279
250
235
255
290
310
260
275
240
Postsession 2665 266
245
240
230
230
235
250
250
215
Let d = presession cholesterol – postsession cholesterol.
Test the null hypothesis that the mean difference equals zero versus the alternative that the
mean difference is positive at  = 0.05. Assume normality.
a. Solve using the p-value approach.
b. Solve using the classical approach.
3. The two independent samples shown in the following table were obtained in order to
estimate the difference between the two population means. Construct the 98% confidence
interval.
Sample A
6
7
7
6
6
5
6
8
5
4
Sample B
7
2
4
3
3
5
4
6
4
2
4.
An article titled "Stages of Change for Reducing Dietary Fat to 30% of Energy or Less"
(Journal of the American Dietetic Association, Vol. 94, No. 10, October 1994) measured the
energy from fat (expressed as a percent) for two different groups. Sample 1 was a random
sample of 614 adults who responded to mailed questionnaires, and sample 2 was a
convenience sample of 130 faculty, staff, and graduate students. The following table gives the
percent of energy from fat for the two groups.
Group
n
Mean
Standard Deviation
1
614
35.0
6.3
2
130
32.0
9.1
a. Construct the 95% confidence interval for 1 - 2.
b. Do these samples satisfy the assumptions for this confidence interval? Explain.
5. A study was designed to compare the attitudes of two groups of nursing students toward
computers. Group 1 had previously taken a statistical methods course that involved significant
computer interaction through the use of statistical packages. Group 2 had taken a statistical
methods course that did not use computers. The students' attitudes were measured by
administering the Computer Anxiety Index (CAIN). The results were as follows:
Group 1 (with computers):
n = 10
s = 7.5
x = 60.3
Group 2 (without computers): n = 15
s = 2.1
x = 67.2
Do the data show that the mean score for those with computer experience was significantly less
than the mean score for those without computer experience? Use  = 0.05.
6. A 1998 study of the Y2K problem investigated consumer opinions over what should be done
to handle the situation and who should be responsible for monitoring the progress. In response
to the question, “Who should monitor the report on progress in solving the Y2K problem?”, 34%
of the respondents surveyed felt that it was the government’s responsibility.
Source: Newsweek, “It’s Not My Problem”, October 5, 1998.
Suppose you believe that differences in opinion exist between rural and city dwellers on whether
the government should monitor the Y2K problem. A study of 250 heads of households in the city
and 200 rural heads of households are asked the above question. You find that 100 of the city
dwellers and 64 of the rural dwellers believed that it was the government’s responsibility. Is
there a significant difference in the opinions of the two groups? Use  = 0.05.
7. One of the most commonly seen applications of statistics is the poll percentages, reported in
the news, of people who say, think or do some specific thing. So who does “know the American
flag?” Two hundred adults in Erie County, NY were asked how many stars there are on the
USA flag. The table below shows the number of adults belonging to each category. The
sample results were tallied twice, by gender and by residence of adult answering question.
n(Knew)
n(Didn’t know)
Men
72
22
Women
72
34
City
57
25
Urban
58
14
Rural
31
15
a. Is there a significant difference between the percentage of men and the percentage of
women who answered the question correctly? Use  = 0.05.
b. Is there a difference between the percentage of city and the percentage of urban adults who
answered the question correctly? Use  = 0.05.
8. Twelve automobiles were selected at random to test two new mixtures of unleaded gasoline.
Each car was given a measured allotment of the first mixture, x, and driven; then the distance
traveled was recorded. The second mixture, y, was immediately tested in the same manner.
The order in which the x and y mixtures were tested was also randomly assigned. The results
are given in the following table.
Car
Mixture
1
2
3
4
5
6
7
8
9
10
11
12
x
7.9
5.6
9.2
6.7
8.1
7.3
8.1
5.4
6.9
6.1
7.1
8.1
y
7.7
6.1
8.9
7.1
7.9
6.7
8.2
5.0
6.2
5.7
6.2
7.5
Can you conclude that there is no real difference in mileage obtained by these two gasoline
mixtures at the 0.10 level of significance? Assume mileage is normal.
a. Solve using the p-value approach.
b. Solve using the classical approach.
9.
The following data were collected concerning waist sizes of men and women. Do these
data present sufficient evidence to conclude that men have larger mean waist sizes than women
at the 0.05 level of significance? Assume waist sizes are normally distributed.
Men
33
34
Women 22
27
33
32
29
26
30
35
27
27
34
32
24
26
34
32
28
25
40
34
28
35
36
35
30
32
38
Chapter 11
1. A nationwide survey of consumers in 1998 was conducted to determine the level of
uncertainty surrounding the Y2K problem. CIO Communications, Inc. asked heads of
households, “What are you planning to do with your money if the Y2K problem isn’t solved by
mid-1999?” The results are shown in the table below:
Plans for Money (National)
Hide it (mattress stuffing)
Deposit it in several banks
Deposit it in one bank
Don’t know
Total
Percent Responding
25
11
16
48
100
Source: Newsweek, “Don’t Bank on It”, August 24, 1998, p. 9.
Suppose a local follow-up survey is conducted using 300 respondents from your city who
answer exactly the same question. Results from the follow-up study are tabulated below:
Plans for Money (Local)
Hide it (mattress stuffing)
Deposit it in several banks
Deposit it in one bank
Don’t know
Total
Number Responding
72
32
47
149
300
Does the distribution of responses differ from the distribution obtained from the nationwide
survey? Test at the 0.05 level of significance.
a. Solve using the p-value approach.
b. Solve using the classical approach.
2. An article titled "Human Papillomavirus Infection and Its Relationship to Recent and Distant
Sexual Partners" (Obstetrics & Gynecology, November 1994) gave the following results
concerning age and the percent who were HPV-positive among the 290 participants in the
study.
Age
N
HPV-Positive (%)
 20
27
40.7
21-25
81
37.0
26-30
108
31.5
31-35
74
24.3
Complete the test of the hypothesis that the same proportion of each age group is HPV-positive
for the population this sample represents. Use 05.
a. Solve using the p-value approach.
b. Solve using the classical approach.
ple show that the median score for the exam is less than 50? Use = 0.05.