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MATH 103/GRACEY
PRACTICE EXAM/CHAPTERS 1-3
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use common sense to determine whether the given event is impossible; possible, but very unlikely; or possible and
likely.
1) Andrew rolled a die five times and got a six every time.
1)
A) Possible and likely
B) Possible, but very unlikely
C) Impossible
2) Lori rolled three dice and got a total of 2.
A) Possible, but very unlikely
B) Possible and likely
C) Impossible
2)
3) When Amina took a four-day Thanksgiving vacation in Seattle, it rained every day.
A) Possible, but very unlikely
B) Impossible
C) Possible and likely
3)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
4) Use the data in the table to answer the question. The x-values are amounts of saturated fat
(in grams) in various regular two-ounce muffins. The y-values are amounts of saturated
fat (in grams) in various "low fat" two-ounce muffins.
Amounts of Saturated Fat in Regular and Low-Fat Muffins
x 5.8
6.5
4.2
5.7
5.2
3.8
y 1.2
2.1
2.1
0.7
2.2
0.9
Is each x-value matched with a corresponding y-value? That is, is each x-value associated
with the corresponding y-value in some meaningful way? If the x- and y-values are not
matched, does it make sense to use the difference between each x-value and the y-value
that is in the same column?
5) The table shows the weights, in pounds, of seven subjects before and after following a
particular diet for two months. Assume that the x-values are the weights before the diet
and the y-values are the weights after the diet.
Subject
A
B
C
D
E
F
G
Before 195 159 167
169 162 166 174
After 188 150 165
174 148 168 162
Are the x-values matched with the corresponding y-values? That is, is each x-value
associated with the corresponding y-value in some meaningful way? If the x- and
y-values are matched, does it make sense to use the difference between each x-value and
the y-value that is in the same column? Why or why not?
1
4)
5)
Form a conclusion about statistical significance. Do not make any formal calculations. Either use the results provided or
make subjective judgments about the results.
6) Charlie's teacher claims that he does not study and just guesses on exams. On an exam
6)
with 201 true-false questions, Charlie answered 53.7% of the questions correctly.
Calculations using these results show that if he were really just guessing, there would be
roughly 1 chance in 7 that he would do this well. Is there statistically significant evidence
against the teacher's claim that Charlie is just guessing? Why or why not?
Provide an appropriate response.
7) An article stated that last year 807 people taking a certain medication suffered from serious
side effects while this year, after the medication had been modified, only 391 suffered
serious side effects. What information is missing? Why would it be important to include
this information?
7)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the given value is a statistic or a parameter.
8) A sample of 120 employees of a company is selected, and the average age is found to be 37 years.
A) Statistic
B) Parameter
9) After taking the first exam, 15 of the students dropped the class.
A) Parameter
B) Statistic
9)
10) A health and fitness club surveys 40 randomly selected members and found that the average
weight of those questioned is 157 lb.
A) Statistic
B) Parameter
Determine whether the given value is from a discrete or continuous data set.
11) The number of freshmen entering college in a certain year is 621.
A) Discrete
B) Continuous
12) The temperature of a cup of coffee is 67.3°F.
A) Discrete
8)
10)
11)
12)
B) Continuous
13) The number of limbs on a 2-year-old oak tree is 21.
A) Continuous
13)
B) Discrete
14) The weight of Bill's pack as he sets off on a backpacking trip is 48.3 lb.
A) Discrete
B) Continuous
14)
Determine which of the four levels of measurement (nominal, ordinal, interval, ratio) is most appropriate.
15) The temperatures of eight different plastic spheres.
A) Ordinal
B) Ratio
C) Nominal
D) Interval
16) The sample of spheres categorized from softest to hardest.
A) Ratio
B) Nominal
C) Interval
D) Ordinal
17) Salaries of college professors.
A) Ordinal
B) Nominal
D) Interval
15)
16)
17)
C) Ratio
2
18) Temperatures of the ocean at various depths.
A) Nominal
B) Ratio
18)
C) Interval
D) Ordinal
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Identify the sample and population. Also, determine whether the sample is likely to be representative of the population.
19) An employee at the local ice cream parlor asks three customers if they like chocolate ice
19)
cream.
Use critical thinking to develop an alternative conclusion.
20) A study shows that adults who work at their desk all day weigh more than those who do
not. Conclusion: Desk jobs cause people to gain weight.
20)
Use critical thinking to address the key issue.
21) An airline company advertises that 100% of their flights are on time after checking 5
randomly selected flights and finding that these 5 were on time.
21)
22) You plan to make a survey of 200 people. The plan is to talk to every 10th person coming
out of the school library. Is there a problem with your plan?
22)
23) A researcher published this survey result: "74% of people would be willing to spend 10
percent more for energy from a non-polluting source". The survey question was
announced on a national radio show and 1,200 listeners responded by calling in. What is
wrong with this survey?
23)
24) A company accused of downsizing workers defended itself with the following statement:
"Yes, we were forced to lay off 20% of our workforce last year, but this year we increased
our workforce by 20%, and we therefore now have the same number of employees as
before the layoff." What is the flaw in this argument?
24)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Perform the requested conversions. Round decimals to the nearest thousandth and percents to the nearest tenth of a
percent, if necessary.
4
25) Convert the fraction to an equivalent decimal and percentage.
25)
9
A) 0.444, 44.4%
B) 0.564, 56.4%
C) 0.444, 4.44%
D) 0.564, 564%
26) Convert 0.6 to an equivalent fraction and percentage.
2
3
2
A) , 6%
B) , 60%
C) , 60%
5
5
5
3
D) , 6%
5
26)
27) Convert 0.296 to an equivalent fraction and percent.
36
37
36
A)
, 29.6%
B)
, 29.6%
C)
, 2.96%
125
125
125
37
D)
, 2.96%
125
28) Convert 2.5 to an equivalent fraction and percent.
1
A) 2 , 25%
B) 2, 25%
2
1
D) 2 , 250%
2
27)
28)
C) 2, 250%
3
Solve the problem.
29) A gardener has 78 clients, 10% of whom are businesses. Find the number of business clients.
A) 8 clients
B) 10 clients
C) 76 clients
D) 70 clients
29)
30) Alex and Juana went on a 116-mile canoe trip with their class. On the first day they traveled 29
miles. What percent of the total distance did they canoe?
A) 0.25%
B) 400%
C) 25%
D) 4%
30)
31) On a test, 86% of the questions are answered correctly. If 215 questions are correct, how many
questions are on the test?
A) 250
B) 86
C) 43
D) 40
31)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
32) A bus company claims that in the past year it has reduced the number of late departures of
buses by 100%. What is wrong with this statement?
32)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the given description corresponds to an observational study or an experiment.
33) A marketing firm does a survey to find out how many people use a product. Of the one hundred
people contacted, fifteen said they use the product.
A) Observational study
B) Experiment
33)
34) A clinic gives a drug to a group of ten patients and a placebo to another group of ten patients to
find out if the drug has an effect on the patients' illness.
A) Observational study
B) Experiment
34)
35) A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided.
A) Observational study
B) Experiment
35)
36) A doctor performs several diagnostic tests to determine the reason for a patient's illness.
A) Observational study
B) Experiment
36)
Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
37) 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348,
and 481 students respectively.
A) Cluster
B) Random
C) Systematic
D) Stratified
E) Convenience
38) A sample consists of every 49th student from a group of 496 students.
A) Convenience
B) Random
C) Stratified
D) Cluster
E) Systematic
4
37)
38)
39) A pollster uses a computer to generate 500 random numbers, then interviews the voters
corresponding to those numbers.
A) Random
B) Cluster
C) Convenience
D) Stratified
E) Systematic
39)
40) An education researcher randomly selects 48 middle schools and interviews all the teachers at each
school.
A) Systematic
B) Random
C) Convenience
D) Stratified
E) Cluster
40)
41) A researcher interviews 19 work colleagues who work in his building.
A) Stratified
B) Convenience
C) Systematic
D) Cluster
E) Random
41)
Provide an appropriate response.
42) An education expert is researching teaching methods and wishes to interview teachers from a
particular school district. She randomly selects ten schools from the district and interviews all of the
teachers at the selected schools. Does this sampling plan result in a random sample? Simple
random sample? Explain.
A) No; no. The sample is not random because teachers in small schools are more likely to be
selected than teachers in larger schools. It is not a simple random sample because some
samples are not possible, such as a sample that includes teachers from schools that were not
selected.
B) Yes; yes. The sample is random because all teachers have the same chance of being selected. It
is a simple random sample because all samples have the same chance of being selected.
C) Yes; no. The sample is random because all teachers have the same chance of being selected. It
is not a simple random sample because some samples are not possible, such as a sample that
includes teachers from schools that were not selected.
D) No; yes. The sample is not random because teachers in small schools are more likely to be
selected than teachers in larger schools. It is a simple random sample because all samples
have the same chance of being selected.
5
42)
43) A researcher obtains an alphabetical list of the 2560 students at a college. She uses a random
number generator to obtain 50 numbers between 1 and 2560. She chooses the 50 students
corresponding to those numbers. Does this sampling plan result in a random sample? Simple
random sample? Explain.
A) No; yes. The sample is not random because not all students have the same chance of being
selected. It is a simple random sample because all samples of 50 students have the same
chance of being selected.
B) Yes; yes. The sample is random because all students have the same chance of being selected. It
is a simple random sample because all samples of 50 students have the same chance of being
selected.
C) No; no. The sample is not random because not all students have the same chance of being
selected. It is not a simple random sample because some samples are not possible, such as a
sample containing the the first 50 students on the list.
D) Yes; no. The sample is random because all students have the same chance of being selected. It
is not a simple random sample because some samples are not possible, such as a sample
containing the first 50 students on the list.
Identify the type of observational study (cross-sectional, retrospective, prospective).
44) A statistical analyst obtains data about ankle injuries by examining a hospital's records from the
past 3 years.
A) Cross-sectional
B) Prospective
C) Retrospective
D) None of these
43)
44)
45) A researcher plans to obtain data by following those in cancer remission since January of 2005.
A) Prospective
B) Cross-sectional
C) Retrospective
D) None of these
45)
46) A town obtains current employment data by polling 10,000 of its citizens this month.
A) Prospective
B) Cross-sectional
C) Retrospective
D) None of these
46)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
47) In a clinical trial for a new headache medication, participants are randomly assigned to a
treatment group or a placebo group. They do not know whether they are receiving the
medication or a placebo. However the doctors administering the medication and
evaluating the results do know which participants are receiving the medication. This
experiment is blind but not double blind. Explain what this means and why the absence of
double blinding could cause a problem.
47)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
48) The frequency distribution below summarizes employee years of service for Alpha Corporation.
Determine the width of each class.
Years of service Frequency
1-5
5
6-10
20
11-15
25
16-20
10
21-25
5
26-30
3
A) 10
B) 6
C) 5
6
D) 4
48)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
49) Using a strict interpretation of the relevant criteria characterizing a normal
distribution,does the frequency distribution below appear to have a normal distribution?
Does the distribution appear to be normal if the criteria are interpreted very loosely?
49)
Closing Share
Price
Frequency
0-5
2
6-10
5
11-15
16
16-20
28
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct the cumulative frequency distribution that corresponds to the given frequency distribution.
50)
Number
Speed of cars
0-29
4
30-59
16
60-89
60
90-119
20
A)
B)
Speed
Less than 30
Less than 60
Less than 90
Less than120
Cumulative
Frequency
4
20
80
100
C)
Speed
Less than 30
Less than 60
Less than 90
Less than120
Cumulative
Frequency
0.04
0.20
0.80
1.00
Speed
Less than 30
Less than 60
Less than 90
Less than120
Cumulative
Frequency
100
80
82
4
D)
Cumulative
Speed Frequency
0-29
4
30-59
20
60-89
80
90-119
100
7
50)
Provide an appropriate response.
51) The frequency distribution for the weekly incomes of students with part-time jobs is given below.
Construct the corresponding relative frequency distribution. Round relative frequencies to the
nearest hundredth of a percent if necessary.
Income ($) Frequency
200-300
68
301-400
69
401-500
79
501-600
87
More than 600
11
A)
Relative
Income ($) Frequency
201-300
15.5%
301-400
22.1%
401-500
31.3%
501-600
16.2%
More than600
14.9%
C)
Relative
Income ($) Frequency
200-300
12.5%
301-400
20.1%
401-500
37.3%
501-600
15.2%
More than 600
14.9%
B)
Relative
Income ($) Frequency
200-300
24.76%
301-400
27.97%
401-500
3.53%
501-600
21.38%
More than 600
24.84%
D)
Income ($)
200-300
301-400
401-500
501-600
More than 600
Relative
Frequency
21.66%
21.97%
25.16%
27.71%
3.50%
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Use the given data to construct a frequency distribution.
52) A medical research team studied the ages of patients who had strokes caused by stress. The 52)
ages of 34 patients who suffered stress strokes were as follows.
29 30 36 41 45 50 57 61 28 50 36 58
60 38 36 47 40 32 58 46 61 40 55 32
61 56 45 46 62 36 38 40 50 27
Construct a frequency distribution for these ages. Use 8 classes beginning with a lower class
limit of 25.
Age Frequency
8
51)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Provide an appropriate response.
53) A nurse measured the blood pressure of each person who visited her clinic. Following is a
relative-frequency histogram for the systolic blood pressure readings for those people aged
between 25 and 40. The blood pressure readings were given to the nearest whole number.
Approximately what percentage of the people aged 25-40 had a systolic blood pressure reading
between 110 and 139 inclusive?
A) 59%
B) 39%
C) 75%
D) 89%
54) The histogram below represents the number of television sets per household for a sample of U.S.
households. How many households are included in the histogram?
50
Frequency
40
30
20
10
1
2
3
4
5
Number of TV Sets
A) 110
B) 95
C) 90
9
53)
D) 100
54)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
55) In a survey, 26 voters were asked their ages. The results are shown below. Construct a
histogram to represent the data (with 5 classes beginning with a lower class limit of 19.5
and a class width of 10). What is the approximate age at the center?
43 56 28 63 67 66 52 48 37 51 40 60 62
66 45 21 35 49 32 53 61 53 69 31 48 59
55)
56) Suppose that you construct a histogram and a relative frequency histogram corresponding
to a particular frequency table. In what ways will the two histograms be similar? In what
ways will they differ?
56)
Solve the problem.
57) The frequency table below shows the amount of weight loss during the first month of a diet
program for both males and females. Compare the results by constructing two frequency
polygons on the same axes, and determine whether there appears to be a significant
difference between the two genders.
Weight (lb)
5-7
8-10
11-13
14-16
17-19
20-22
Frequency (males)
2
9
18
13
4
1
Weight (lb)
5-7
8-10
11-13
14-16
17-19
20-22
20
18
16
14
12
10
8
6
4
2
5
10
15
20
25
10
Frequency (females)
4
3
19
5
15
1
57)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Construct the dotplot for the given data.
58) Attendance records at a school show the number of days each student was absent during the year.
The days absent for each student were as follows.
0 2 3 4 2 3 4 6 7 2 3 4 6 9 8
A)
B)
C)
D)
Use the data to create a stemplot.
59) The attendance counts for this season's basketball games are listed below.
227 239 215 219
221 233 229 233
235 228 245 231
A)
B)
21 5 9
21 5 7 9
22 1 7 8 9
22 1 8 9
23 1 3 3 5 9
23 1 3 3 5 9
24 5
24 5
11
58)
59)
60) The following data consists of the weights (in pounds) of 15 randomly selected women and the
weights of 15 randomly selected men. Construct a back-to-back stemplot for the data.
Women: 128
122
145
Men:
140
136
173
Men
A) 1
5 3
9 6
6
9
9
6
0
3
2
3
6
6
11
12
13
14
15
16
17
18
19
150
137
126
118
110
139
166
175
111
142
152
170
153
176
190
Women
0 1
2 6 8
7 9
2 5
0 2 4
6
0 5
199
162
141
186
196
166
169
155
153
Men
B)
1
5 3
9 6
6
9 6
Find the original data from the stemplot.
61)
Stem Leaves
6
5 8
7
1 8
8
5 5
A) 61, 65, 61, 78, 88, 85
C) 65, 68, 71, 71, 85, 85
11
12
6 13
0 14
3 15
2 16
3 17
6 18
0 19
60)
Women
0 1 8
2 6 8
7 9
2 5
0 2
6
0 5
61)
B) 65, 61, 68, 71, 81, 85
D) 65, 68, 71, 78, 85, 85
Cumulative
Minutes on Number of Relative
homework students
frequency frequency
0-15
2
0.05
2
16-30
4
0.10
6
31-45
8
0.20
14
46-60
18
0.45
32
61-75
4
0.10
36
76-90
4
0.10
40
Cumulative Frequency
Provide an appropriate response.
62) The table contains data from a study of daily study time for 40 students from Statistics 101.
Construct an ogive from the data.
50
45
40
35
30
25
20
15
10
5
0
15.5 30.5 45.5 60.5 75.5 90.5
Homework Time (minutes)
12
62)
B)
100
90
80
70
60
50
40
30
20
10
0
Relative Frequency
Relative Frequency
A)
100
90
80
70
60
50
40
30
20
10
0
15.5 30.5 45.5 60.5 75.5 90.5
Homework Time (minutes)
15.5 30.5 45.5 60.5 75.5 90.5
Homework Time (minutes)
D)
Frequency
C)
100
90
80
70
60
50
40
30
20
10
0
15.5 30.5 45.5 60.5 75.5 90.5
Homework Time (minutes)
Solve the problem.
63) 240 casino patrons, were interviewed as they left the casino. 72 of them said they spent most of the
time playing the slots. 72 of them said they played blackjack. 36 said they played craps. 12 said
roulette. 12 said poker. The rest were not sure what they played the most. Construct a Pareto chart
to depict the gaming practices of the group of casino goers. Choose the vertical scale so that the
relative frequencies are represented.
13
63)
A)
B)
C)
D)
64) A car dealer is deciding what kinds of vehicles he should order from the factory. He looks at his
sales report for the preceding period. Choose the vertical scale so that the relative frequencies are
represented.
Vehicle Sales
Economy
34
Sports
8.5
Family 59.5
Luxury
17
Truck
51
Construct a Pareto chart to help him decide.
14
64)
A)
B)
C)
D)
Construct a pie chart representing the given data set.
65) The following figures give the distribution of land (in acres) for a county containing 66,000 acres.
Forest Farm Urban
9900 6600 49,500
A)
B)
15
65)
Use the pie chart to solve the problem.
66) A survey of the 4571 vehicles on the campus of State University yielded the following pie chart.
66)
9%
16%
35%
8%
4%
28%
What percent of the vehicles are hatchbacks?
A) 35%
B) 28%
C) 160%
D) 8%
Use the given paired data to construct a scatterplot.
67) x -2 -8 -5 -1 -8 2 -6 6 -4 -2
y -6 -1 -8 2 4 3 -10 4 -2 -6
67)
y
10
-10
10
x
-10
A)
B)
y
y
10
-10
10
10
x
-10
-10
10
-10
16
x
C)
D)
y
y
10
-10
10
10
x
-10
-10
10
x
-10
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
68) Use the high closing values of Naristar Inc. stock from the years 1990 - 2001 to construct a
time-series graph. (Let x = 0 represent 1990 and so on.) Identify a trend.
y
Year High Year High
1990 42 1996 47
1991 40 1997 60
1992 31 1998 61
1993 42 1999 57
1994 44 2000 54
1995 47 2001 30
x
17
68)
69) An annual survey sent to retail store managers contained the question "Did your store
suffer any losses due to employee theft?" The responses are summarized in the table for
two years, 2000 and 2005. Construct a multiple bar graph of the data, then describe any
trends.
69)
Employee Percentage Percentage
Theft
in 2000
in 2005
Yes
49
32
No
51
68
Totals
100
100
70) A television manufacturer sold three times as many televisions in 2005 as it did in 1995. To
illustrate this fact, the manufacturer draws a graph as shown below. The television on the
right is three times as tall and three times as wide as the television on the left. Why is this
graph misleading? What visual impression is created by the graph?
18
70)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the mean for the given sample data. Unless indicated otherwise, round your answer to one more decimal place than
is present in the original data values.
71) The weights (in pounds) of six dogs are listed below. Find the mean weight.
71)
13 21 75 21 134 60
A) 54 lb
B) 53.5 lb
C) 64.8 lb
D) 54.5 lb
Find the median for the given sample data.
72) The ages (in years) of the eight passengers on a bus are listed below.
6 4 25 19 26 49 36 33
Find the median age.
A) 25 yr
B) 25.5 yr
C) 26 yr
D) 24.5 yr
Find the mode(s) for the given sample data.
73) 77 52 32 52 29 77
A) 77
B) 53.2
D) 77, 52
72)
73)
C) 52
Find the midrange for the given sample data.
74) A meteorologist records the number of clear days in a given year in each of 21 different U.S. cities.
The results are shown below. Find the midrange.
72 143 52 84 100 98 101
120 99 121 86 60 59 71
125 130 104 74 83 55 169
A) 112 days
B) 110.5 days
C) 98 days
D) 117 days
74)
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Find the mean and median for each of the two samples, then compare the two sets of results.
75) A comparison is made between summer electric bills of those who have central air and
those who have window units.
May June July Aug Sept
Central $32 $64 $80 $90 $65
Window $15 $84 $99 $120 $40
75)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find the mean of the data summarized in the given frequency distribution.
76) A company had 80 employees whose salaries are summarized in the frequency distribution below.
Find the mean salary.
Salary ($) Employees
5,001-10,000
16
10,001-15,000
14
15,001-20,000
15
20,001-25,000
17
25,001-30,000
18
A) $16,143.75
B) $17,500
C) $17,937.50
19
D) $19,731.25
76)
Solve the problem.
77) A student earned grades of 91, 76, 92, and 79 on her four regular tests. She earned a grade of 79 on
the final exam and 85 on her class projects. Her combined homework grade was 87. The four
regular tests count for 40% of the final grade, the final exam counts for 30%, the project counts for
10%, and homework counts for 20%. What is her weighted mean grade? Round to one decimal
place.
A) 84.2
B) 84.1
C) 82.4
D) 83.4
Find the range for the given sample data.
78) Rich Borne teaches Chemistry 101. Last week he gave his students a quiz. Their scores are listed
below.
22 31 47 29 31 12 48 41 50 56 37 22
A) 44
B) 9
C) 12
D) 56
Find the variance for the given data. Round your answer to one more decimal place than the original data.
79) 19 11 12 7 11
A) 19.0
B) 15.2
C) 49.0
D) 18.9
77)
78)
79)
Find the standard deviation for the given sample data. Round your answer to one more decimal place than is present in
the original data.
80) The top nine scores on the organic chemistry midterm are as follows.
80)
37, 24, 53, 49, 44, 63, 28, 49, 30
A) 13.9
B) 13.0
C) 5.2
D) 12.3
Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal
place.
81) Compare the variation in heights to the variation in weights of thirteen-year old girls. The heights
81)
(in inches) and weights (in pounds) of nine randomly selected thirteen-year old girls are listed
below.
Heights (inches): 59.2 61.4 62.4 64.7 60.1 58.3 64.6 63.7 66.1
Weights (pounds): 86
94
92
119
96
90
123
98
139
A) Heights: 4.4%
Weights: 17.6%
There is substantially more variation in the weights than in the heights of the girls.
B) Heights: 4.1%
Weights: 16.7%
There is substantially more variation in the weights than in the heights of the girls.
C) Heights: 11.5%
Weights: 6.6%
There is substantially more variation in the heights than in the weights of the girls.
D) Heights: 4.6%
Weights: 18.4%
There is substantially more variation in the weights than in the heights of the girls.
20
Find the range, variance, and standard deviation for each of the two samples, then compare the two sets of results.
82) When investigating times required for drive-through service, the following results (in seconds)
82)
were obtained.
Restaurant A 120 67 89 97 124 68 72 96
Restaurant B 115 126 49 56 98 76 78 95
A) Restaurant A: 57 sec; 493.98 sec2 ; 22.23 sec
Restaurant B: 56 sec; 727.98 sec2 ; 32.89 sec
There is more variation in the times for restaurant B.
B) Restaurant A: 57 sec; 493.98 sec2 ; 22.23 sec
Restaurant B: 77 sec; 727.98 sec2 ; 26.98 sec
There is more variation in the times for restaurant B.
C) Restaurant A: 75 sec; 493.98 sec2 ; 22.23 sec
Restaurant B: 70 sec; 727.98 sec2 ; 26.98 sec
There is more variation in the times for restaurant B.
D) Restaurant A: 57 sec; 793.98 sec2 ; 28.18 sec
Restaurant B: 77 sec; 727.98 sec2 ; 26.98 sec
There is more variation in the times for restaurant A.
Find the standard deviation of the data summarized in the given frequency distribution.
83) A company had 80 employees whose salaries are summarized in the frequency distribution below.
Find the standard deviation.
Salary (dollars)
Employees
5,001-10,000
14
10,001-15,000
13
15,001-20,000
18
20,001-25,000
18
25,001-30,000
17
A) $6969.4
B) $7526.9
C) $7317.8
D) $7736.0
Use the range rule of thumb to estimate the standard deviation. Round results to the nearest tenth.
84) The heights in feet of people who work in an office are as follows.
6.0 5.5 5.9 5.4 5.8 5.6 5.7 6.2 5.6 5.6
A) 1.2
B) 0.2
C) 0.1
D) 0.5
Use the empirical rule to solve the problem.
85) The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120
mmHg and a standard deviation of 12 mmHg. What percentage of 18-year-old women have a
systolic blood pressure between 96 mmHg and 144 mmHg?
A) 68%
B) 99.99%
C) 95%
D) 99.7%
Solve the problem.
86) The ages of the members of a gym have a mean of 47 years and a standard deviation of 10 years.
What can you conclude from Chebyshev's theorem about the percentage of gym members aged
between 32 and 62?
A) The percentage is at most 55.6%
B) The percentage is approximately 33.3%
C) The percentage is at least 33.3%
D) The percentage is at least 55.6%
21
83)
84)
85)
86)
Solve the problem. Round results to the nearest hundredth.
87) Scores on a test have a mean of 75 and a standard deviation of 9. Michelle has a score of 84.
Convert Michelle's score to a z-score.
A) -9
B) -1
C) 9
D) 1
88) A department store, on average, has daily sales of $28,993.06. The standard deviation of sales is $
1000. On Tuesday, the store sold $34,199.86 worth of goods. Find Tuesday's z score. Was Tuesday
an unusually good day?
A) 5.52, yes
B) 5.21, yes
C) 5.47, no
D) 4.17, no
Find the number of standard deviations from the mean. Round your answer to two decimal places.
89) The test scores on the Chapter 7 mathematics test have a mean of 66 and a standard deviation of 13.
Andrea scored 89 on the test. How many standard deviations from the mean is that?
A) 1.77 standard deviations above the mean
B) 1.77 standard deviations below the mean
C) 0.60 standard deviations below the mean
D) 0.60 standard deviations above the mean
87)
88)
89)
Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual.
Consider a score to be unusual if its z-score is less than -2.00 or greater than 2.00. Round the z-score to the nearest tenth
if necessary.
90) A body temperature of 96.5° F given that human body temperatures have a mean of 98.20° F and a
90)
standard deviation of 0.62°.
A) -2.8; unusual
B) -1.7; not usual
C) -2.8; not unusual
D) 2.8; unusual
Determine which score corresponds to the higher relative position.
91) Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score
of 688 on a test with a mean of 493 and a standard deviation of 150?
A) Both scores have the same relative position.
B) A score of 688
C) A score of 92
Find the percentile for the data value.
92) Data set: 53 45 39 69 66 72 44;
data value: 53
A) 20
B) 50
91)
92)
C) 43
D) 57
Find the indicated measure.
93) Use the given sample data to find Q3 .
93)
49 52 52 52 74 67 55 55
A) 6.0
B) 67.0
C) 61.0
22
D) 55.0
Construct a boxplot for the given data. Include values of the 5-number summary in all boxplots.
94) The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below.
Construct a boxplot for the data set.
310 320 450 460 470 500 520 540
580 600 650 700 710 840 870 900
1000 1200 1250 1300 1400 1720 2500 3700
A)
B)
C)
94)
D)
Construct a modified boxplot for the data. Identify any outliers.
95) The weights (in ounces) of 27 tomatoes are listed below.
1.7 2.0 2.2 2.2 2.4 2.5 2.5 2.5 2.6
2.6 2.6 2.7 2.7 2.7 2.8 2.8 2.8 2.9
2.9 2.9 3.0 3.0 3.1 3.1 3.3 3.6 4.2
A) Outliers: 1.7 oz, 3.6 oz, 4.2 oz
B) Outlier: 4.2 oz
C) No outliers
D) Outliers: 1.7 oz, 4.2 oz
23
95)
Provide an appropriate response.
96) For data which are heavily skewed to the right, P10 is likely to be closer to the median than P90.
True or false?
A) True
96)
B) False
97) If all the values in a data set are converted to z-scores, the shape of the distribution of the z-scores
will be bell-shaped regardless of the distribution of the original data. True or false?
A) True
B) False
97)
98) In a data set containing n values, the 67th percentile can be found as follows:
98)
P67 =
67
· n.
100
True or false?
A) False
B) True
99) Which of the following statements regarding percentiles is true? (More than one statement may be
true).
A : In any data set, P90 is greater than P80
B: In any data set,
P10 + P90
2
is equal to Q2
C: In a set of 20 test scores, the percentile of the second highest score is 95
A) B
B) A
C) C
24
D) All of the above
99)
Answer Key
Testname: PRACTICE EXAM 1
1)
2)
3)
4)
B
C
C
The x-values are not matched with the y-values, so it does not make sense to use the differences between each x-value
and the y-value that is in the same column.
5) The x-values are matched with the corresponding y-values. It makes sense to use the difference between each x-value
and the y-value that is in the same column. Both represent weights measured in pounds and both are associated with
the same person. The x-value is the weight of a person before the diet and the y-value in the same column is the
weight of the same person after the diet. The difference represents the amount of weight lost (or gained) by that
person.
6) No; The exam result of 53.7% is not substantially greater than 50%. Even if Charlie were just guessing, he could easily
do this well just by chance.
7) There is no context to the data. The article should include the number of people taking the medication last year and
this. More important than the number suffering serious side effects is the percentage of those taking the medication
that suffer side effects. Although fewer people suffered side effects this year, it is possible (if fewer people are taking
the medication this year) that the percentage suffering side effects has actually increased.
8) A
9) A
10) A
11) A
12) B
13) B
14) B
15) D
16) D
17) C
18) C
19) Sample: the 3 selected customers; population: all customers; not representative
20) Desk job workers are confined to their chairs for most of their work day. Other jobs require standing or walking
around which burns calories. It is probably the lack of exercise that causes higher weights, not the desk job itself. Avoid
causality altogether by saying lack of walking and exercise is associated with higher weights.
21) The sample was too small.
22) People who don't go to the library are excluded.
23) This is a voluntary response sample. The survey is based on voluntary, self-selected responses and therefore has
serious potential for bias.
24) Answers will vary. Possible answer: This is a misleading use of percentages, as 20% of the reduced workforce is
smaller than 20% of the original workforce. The company therefore did not hire as many new workers as it originally
laid off. The size of the current workforce is therefore smaller than the size of the workforce before the layoffs.
25) A
26) B
27) B
28) D
29) A
30) C
31) A
32) A reduction of 100% would mean that the company had reduced the number of late departures to zero which is not
plausible.
33) A
34) B
35) A
25
Answer Key
Testname: PRACTICE EXAM 1
36) B
37) D
38) E
39) A
40) E
41) B
42) C
43) B
44) C
45) A
46) B
47) This experiment is blind because participants do not know whether they are receiving the treatment or a placebo. This
will allows investigators to determine whether the treatment effect is significantly different from the placebo effect.
However, the experiment is not double blind because the doctors administering the medication and evaluating the
results know which participants are receiving the medication. The doctors may not be impartial and their evaluation
and analysis of results could be influenced by their knowledge of which participants are receiving the treatment.
48) C
49) No; no; The frequencies do not increase, reach a maximum, and then decrease.
50) A
51) D
52)
Age Frequency
25-29
3
30-34
3
35-39
6
40-44
4
45-49
5
50-54
3
55-59
5
60-64
5
53) C
54) D
55) The approximate age at the center is 50.
56) The two histograms will have the same shape. They will also have the same scale on the horizontal axis. They will
differ only in the scales on the vertical axis: the histogram will show frequencies on the vertical axis while the relative
frequency histogram will show relative frequencies.
26
Answer Key
Testname: PRACTICE EXAM 1
57) There does not appear to be a significant difference.
20
freq
18
16
14
12
10
8
6
4
2
5
10
15
25 weight
20
58) B
59) A
60) B
61) D
62) C
63) C
64) A
65) B
66) A
67) D
68) Trend: Answers will vary. Possible answer: High closing stock values show a decrease from 1990 through 1992, after
which the value of the stock rose through 1998. Another decrease occurred in 1999 and continued through 2001.
y
80
70
60
50
40
30
20
10
1
2
3
4
5
6
7
8
9 10 11 x
27
Answer Key
Testname: PRACTICE EXAM 1
69) Losses due to employee theft have decreased from 2000 to 2005.
70) The area of the television on the right is nine times (not three times) the area of the television on the left. The graph
gives the visual impression that sales in 2005 were nine times the sales in 1995.
71) A
72) B
73) D
74) B
75) Central air: mean = $66.20; median = $65
Window unit: mean = $71.60; median = $84
Window units appear to be significantly more expensive.
76) C
77) D
78) A
79) A
80) B
81) A
82) B
83) A
84) B
85) C
86) D
87) D
88) B
89) A
90) A
91) C
92) C
93) C
94) D
95) D
96) A
97) B
98) A
99) B
28