Name: ________________________ Class: ___________________ Date: __________
ID: A
Sample Mastery Questions Test 1
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. A population refers to
a. a portion of a group about which data are being collected
b. the number of individuals in a group
c. the entire group about which data are being collected
d. the number of individuals within a given category
____
2. Simone surveys her class to determine the number of siblings for each student. The most appropriate method
for displaying her data would be a
a. broken-line graph
c. stem-and-leaf plot
b. histogram
d. bar graph
____
3.
For the data represented in the above box-and-whisker plot, the median of the upper half of the data is
a. 17
c. 24
b. 21
d. 27
____
4. A bar graph is most appropriate for describing
a. the frequency distribution of discrete data
b. the frequency distribution of continuous data
c. changes of data over time
d. the median of a set of data
____
5. A set of data has values ranging from 420 to 2150. The most appropriate spread for a class interval is
a. 50
c. 200
b. 173
d. 800
____
6. In a sample of 50 high school students, 15 said that math was their favourite subject. If these data were
represented in a circle graph, the corresponding sector angle would be
a. 15°
c. 54°
b. 30°
d. 108°
____
7. A broken-line graph is best used to describe
a. the frequency of a data category
b. trends of the data over time
c.
d.
1
the spread of data
the percentage of data in each category
Name: ________________________
____
____
ID: A
8. A census gathers information from
a. a specific group within a population
b. all individuals in a population
c.
d.
a random sample of a population
the population over many years
9. A graph in which data are organized into equal class intervals along the horizontal axis is a
a. pictograph
c. bar graph
b. broken-line graph
d. histogram
____ 10. In a stem-and-leaf plot, the leaves represent the
a. frequency of a data category
b. final digits of the values in a data category
c. initial digits of a data category
d. average of the data values
____ 11. The following pictograph depicts the population of selected provinces.
Province
Population
Ontario
Quebec
B.C.
Nova Scotia
Which of the following statements can be concluded?
a. the population of Quebec is 700 000
b. Nova Scotia is the least populated province in Canada
c. the population of Ontario is approximately double that of B.C.
d. the population of Quebec is increasing
____ 12. The median of a set of data refers to the
a. average of all data values
b. data value with the greatest frequency
c. spread of the data values
d. middle term in the frequency distribution
____ 13. A class interval refers to
a. a division used for grouping a set of observations
b. the range of ages among a group of students
c. the number of categories within a group of data
d. the spread of values within an individual category
____ 14. A frequency table is used to
a. represent data in a graphical format
b. list variables and their frequencies
c. analyze the change in frequencies over time
d. illustrate the median and spread of a set of data
2
Name: ________________________
ID: A
____ 15. In a circle graph, the sum of the sector angles is
a. 360°
c.
b. 100°
d.
180°
the sum of the frequencies
____ 16. A split-bar graph can be used to
a. compare category frequencies of different genders
b. compare category frequencies for different years
c. compare category frequencies for different locations
d. all of the above
____ 17. A causal relationship means that
a. two variables have a positive correlation
b. two variables have a negative correlation
c. two variables are unrelated
d. one variable directly affects another
____ 18. The following graph summarizes scoring by different positions on a hockey team.
Which of the following is not a valid conclusion?
a. there were fewer goals than assists
b. defense scored fewer points than forwards
c. the defense had a higher ratio of goals to assists
d. the defense had fewer assists than the forwards
3
Name: ________________________
ID: A
____ 19. The following graph illustrates participation in various sports by students at a high school.
Which sport has the greatest proportion of females?
c. basketball
a. football
b. swimming
d. gymnastics
____ 20. Jason has a theory that left-handed golfers are better than right-handed golfers. He records the scores of several
players and displays the results in the following graph.
Which of the following statements is not true?
a. there were more right-handed golfers than left-handed golfers
b. left-handed golfers shot a lower percentage of above par scores than right-handed golfers
c. right-handed golfers shot a lower percentage of above par scores than left-handed golfers
d. right-handed golfers scored above par more often than par or lower
4
Name: ________________________
ID: A
____ 21. The following graph illustrates the trends in urban vs. rural population in Canada.
Which of the following conclusions can be made?
a. the total population is staying the same
b. the rural population is decreasing
c. soon there will be no rural population
d. the percentage of the urban population is increasing
____ 22. Students at a high school were asked which was their favourite subject. The results are shown in the following
graph.
Which subject is most popular among female students?
a. Music
c. Science
b. Phys-Ed
d. English
5
Name: ________________________
ID: A
____ 23. The owner of a video store has tracked the average number of weekly VHS and DVD rentals. The results are
shown in the following graph.
Which of the following statements is true?
a. the total number of rentals is declining
b. there are more DVD rentals than VHS rentals
c. the number of VHS rentals is decreasing
d. the proportion of VHS rentals is decreasing
____ 24. Samantha surveys the students in her class and finds that the average math mark of females is higher than that
of males. She concludes that females are better in math than males. Samantha's study is flawed because
a. she did not ask for the students' marks in other courses
b. her sample size was not large enough
c. she did not say how much higher was the females’ average mark
d. she did not draw a graph
6
Name: ________________________
ID: A
____ 25. What conclusion is valid based on the above data?
a. a person's educational achievement is independent of their parents'
b. a person's educational achievement is usually the same as their parents'
c. having smart parents makes you smart
d. there is a correlation between the educational achievement of parents and their children
____ 26. Lisa asked the students in her class if they played basketball and also if they played volleyball. Her results are
summarized below.
Which of the following conclusions is valid?
a. students who play basketball are not likely to play volleyball
b. more students play basketball than volleyball
c. students who play volleyball are likely to also play basketball
d. there is no correlation between playing basketball and volleyball
7
Name: ________________________
ID: A
____ 27. Students were asked whether or not they enjoyed math class and English class. The results are shown in the
following graph.
Which of the following conclusions is not valid?
a. most students enjoy math
b. most students enjoy English
c. students who enjoy math are less likely to enjoy English than those who do not enjoy math
d. there is no correlation between enjoying math and English
____ 28. Students at a high school were asked if they ever rode a bicycle to school. The results are shown in the
following graph.
Which of the following conclusions is valid?
a. most males ride a bicycle to school
b. females are less likely to bike to school
c. males are less likely to bike to school
d. there is no relationship between gender and biking to school
8
Name: ________________________
ID: A
____ 29. Students were asked whether they would prefer a cat or a dog for a pet. The results are shown in the following
graph.
Which of the following conclusions is valid?
a. females are more likely to prefer cats over dogs
b. most students prefer cats
c. males and females are equally likely to prefer dogs
d. there is no correlation between gender and pet preference
____ 30. Carrie conducted a survey to determine if there is a relationship between reading for pleasure and doing well in
English class.
Which of the following conclusions is not valid?
a. most students read for pleasure
b. most students do well in English
c. there is no correlation between reading for pleasure and doing well in English
d. students who read for pleasure are more likely to do well in English
____ 31. Which of the following is not true about a dependent variable?
a. a dependent variable is determined from the independent variable
b. a dependent variable is represented on the vertical axis of a graph
c. a dependent variable represents the frequency of the independent variable
d. a dependent variable may take on the same value for 2 different data points
9
Name: ________________________
ID: A
____ 32. In the following graph, what type of correlation is indicated?
a.
b.
strong positive
strong negative
c.
d.
weak positive
weak negative
____ 33. In the following graph, what type of correlation is indicated?
a.
b.
strong positive
strong negative
c.
d.
weak positive
weak negative
____ 34. The variables student height and grade in mathematics have
a. a positive correlation
c. an inverse correlation
b. a negative correlation
d. no correlation
____ 35. Two variables have a strong negative correlation. Which of the following statements is not true?
a. the dependent variable decreases as the independent variable increases
b. the trend of the data exhibits an irregular decline
c. the line of best fit has a negative slope
d. most data points lie close to the line of best fit
10
Name: ________________________
ID: A
____ 36. A line of best fit
a. must pass through the origin
b. must pass through the median of the data
c. must have a positive slope
d. represents the trend of the data
____ 37. The median-median line
a. only passes through key points based on medians
b. passes through the median x-value and median y-value of the data
c. is another name for the line of best fit
d. is used when there is no correlation between the variables
____ 38. The amount of time spent studying for a math test and the mark achieved would most likely exhibit
a. a positive correlation
c. no correlation
b. a negative correlation
d. a dependent trend
____ 39. A pattern of average behaviour that occurs over time is
a. a positive correlation
c. a trend
b. a dependent variable
d. a line of best fit
____ 40. The horizontal axis usually represents the
a. time
b. frequency
c.
d.
dependent variable
independent variable
____ 41. If two variables have no correlation
a. the line of best fit has a slope of zero
b. a median-median line must be used to predict trends
c. the line of best fit has a negative slope
d. the points on a scatter plot appear to be random
____ 42. What type of correlation would exist between the number of hotdogs that a vendor sells and the price charged
per hotdog?
a. positive correlation
c. no correlation
b. negative correlation
d. quadratic correlation
____ 43. What type of correlation would exist between a person's height and her or his stride length?
a. positive correlation
c. no correlation
b. negative correlation
d. inverse correlation
____ 44. Two variables have a weak negative correlation. Which of the following statements is most accurate?
a. the line of best fit must have a small positive slope
b. the line of best fit must have a small negative slope
c. the data points lie very close to the line of best fit
d. many data points do not lie very close to the line of best fit
11
Name: ________________________
ID: A
____ 45. What type of correlation exists in the following scatter plot?
a.
b.
weak positive
strong positive
c.
d.
weak negative
strong negative
____ 46. The regression associated with a set of data
a. is always linear
b. is always quadratic
c. may be linear or quadratic
d. may be modelled with any type of function
____ 47. Two variables have a correlation coefficient of r = 0.9. This indicates
a. a strong positive correlation
c. a strong negative correlation
b. a weak positive correlation
d. a weak negative correlation
____ 48. If two variables have no correlation, their correlation coefficient would have a value of
c. 100
a. +1
b. −1
d. 0
____ 49. Two variables have a coefficient of determination of 0.64. The correlation coefficient could be
a. −0.64
c. −0.8
b. 0.41
d. 0.36
____ 50. A relationship in which all data values lie on the regression line has a correlation coefficient of
a. 1
c. −1
b. 0
d. +1 or −1
12
Name: ________________________
ID: A
____ 51. The regression line shown would have a correlation coefficient closest to
a.
b.
+1
0.5
c.
d.
−1
0
____ 52. For the regression line shown, the coefficient of determination would be closest to
a.
b.
+1
0
c.
d.
−1
0.25
____ 53. The residuals for a set of data represent the
a. differences between consecutive x-values
b. vertical differences between data points and the line of best fit
c. data points that lie below the line of best fit
d. data points that do not lie on the line of best fit
____ 54. If a set of data has a very strong correlation, the residual values will be
a. very large
c. negative
b. positive
d. very small
____ 55. A coefficient of determination, r 2 = 0.75, indicates that
a. 75% of the data lie on the regression line
b. the slope of the regression line is 0.75
c. 75% of the variance in y is a result of the variance in x
d. the data have a strong positive correlation
13
Name: ________________________
ID: A
____ 56. Which of the following statements is not true about variables having a correlation coefficient of 1?
a. all data points lie on the line of best fit
b. data points with larger x-values also have larger y-values
c. there is a cause-effect relationship between the variables
d. all of the residual values are zero
____ 57. An agricultural researcher notices a strong positive correlation between the number of lady bugs in a garden
and the growth of the plants. Which of the following statements is not true?
a. if there are fewer lady bugs, then there is less plant growth
b. if there are more lady bugs, then there is more plant growth
c. the coefficient of determination is close to 1
d. the plants cannot grow without the lady bugs
____ 58. What type of correlation would exist between the speed that a person runs and the time required to complete a
race?
a. positive correlation
c. no correlation
b. negative correlation
d. residual correlation
____ 59. Which of the following is an example of a negative correlation?
a. amount of studying and mark on a test
b. temperature and number of kids at a pool
c. a person’s arm length and leg length
d. number of people and slices of pizza per person
____ 60. A set of data having small residual values means that
a. the correlation coefficient is close to 0
b. there is a positive correlation
c. there is a negative correlation
d. there is a strong correlation
____ 61. The purpose of the media is to
a. give their personal opinions on events
b. inform the public about events in an objective manner
c. present data in a way that makes certain groups look favourable
d. create false impressions and sway public opinion
____ 62. Graphs can be misleading because
a. they may use varying scales
b. they may have suggestive captions
c.
d.
they may be based on small samples
all of the above
____ 63. Which of the following statements is not true? The media can influence a person's opinion by
a. using graphs and changing the vertical scale
b. using data taken over a short period of time
c. altering the data to make a better point
d. using data taken from a small sample size
14
Name: ________________________
ID: A
____ 64. The student council decides to survey some students about the music they would like at an upcoming dance. If
there are 1000 students at the school, a reasonable sample size would be
a. 10
c. 100
b. 20
d. 1000
____ 65. Based on the following graphs, which statement is true?
a.
b.
c.
d.
the sale of cars is increasing faster than the sale of minivans
there are more minivans sold than cars
if the current trends continue, eventually there will be more minivans sold than cars
the sale of minivans is increasing more slowly than the sale of cars
____ 66. Which statement is most accurate about the following graph?
a.
b.
c.
d.
the temperature has increased dramatically in the last 100 years
the graph makes the temperature increase seem less than it really is
the temperature has increased slightly in the last 100 years
the graph gives very little information
15
Name: ________________________
ID: A
____ 67. The student council surveys all of the Grade 9 classes to determine what music to play at the next dance. The
results would be flawed because the
a. sample is not representative of the entire population
b. sample size is too small
c. entire school must be surveyed
d. sample is not random
____ 68. The following graph shows the number of points a hockey team had over four seasons. The graph is misleading
because
a.
b.
c.
d.
it does not include years before 1999
it does not indicate the number of games
the vertical scale exaggerates the number of points in 2002
it only shows the points for one team
____ 69. If the vertical scale on a bar graph is changed, incorrect conclusions may be drawn because
a. the heights of the bars are not proportional to the frequencies
b. the frequencies may seem smaller or larger than what they really are
c. the differences between frequencies may seem larger
d. all of the above
____ 70. Consider the following newspaper headline:
"City Residents Oppose New Housing Subdivision"
The headline may be misleading because
a. it does not specify what percentage of residents are opposed
b. it does not specify the number of residents surveyed
c. it does not indicate which residents were surveyed
d. all of the above
____ 71. The statement “60% of Students Find Math Difficult” might be misleading because it does not
a. say what grade the students were in
b. say what level of math they were studying
c. say the number of students that were sampled
d. mention how many thought other subjects were difficult
16
Name: ________________________
ID: A
____ 72. The following graph may be misleading because the
a.
b.
c.
d.
vertical scale has a small range of values
type of coin is not specified
number of tosses is not specified
title is misleading
____ 73. The following graph shows the theatre attendance for three different movies on a particular night.
Which of the following conclusions can be reached from the graph?
a. far more people saw movie C than the others
b. movie C was the most popular movie in the theatre
c. slightly more people saw movie C than movies A or B
d. more people saw movie C than movies A and B combined
17
Name: ________________________
ID: A
____ 74. Based on the following graph, which statement is not correct?
a.
b.
c.
d.
the tuition increased by $50 in 2002
the tuition has increased steadily since 1995
the tuition in 2002 was more than 5 times that of 1995
the greatest increase in tuition occurred in 2001
____ 75. Based on the following graph, which of the statements is false?
a.
b.
c.
d.
the life expectancy of men is increasing
the rate at which the life expectancy is increasing is getting smaller
the life expectancy has increased by over 15 years since 1931
the height of each bar is proportional to the life expectancy
____ 76. A researcher records the marital status and income of a sample of 1143 female executives. The number of
different variables recorded is:
a. 1143
b. three–marital status, income, and number of female executives
c. two–marital status and income
d. 3429
18
Name: ________________________
ID: A
____ 77. A sociologist at a Canadian university wants to study the attitudes of female university students towards
careers. He interviews 100 of the female students enrolled in a first-year sociology course at his university.
What is the sample in this situation?
a. Canadian female university students
b. the 100 female students interviewed
c. the female students taking this course
d. all Canadian women taking first-year sociology
____ 78. A sociologist at a Canadian university wants to study the attitudes of female university students in Canada
towards careers. He interviews 100 of the female students enrolled in a first-year sociology course at his
university. What is the population in this situation?
a. Canadian female university students
b. the 100 female students interviewed
c. the female students taking this course
d. all women in Canada taking first-year sociology
____ 79. Data collection is often carried out on samples because
a. an appropriate sample can be used to make inferences about the population
b. the population is often not available
c. neither a nor b
d. both a and b
____ 80. When can the value of a quantitative variable be expressed as a number?
a. never
c. only if the variable is discrete
b. only if the variable is continuous
d. always
____ 81. The size of a building can be measured many ways. Here are four examples: the floor area in square metres, the
number of stories, the height of the building, the number of rooms. What is true about these variables?
a. some are qualitative and some are quantitative
b. all are quantitative and continuous
c. all are qualitative and some are continuous and some are discrete
d. all are quantitative and some are continuous and some are discrete
____ 82. Each of the following variables affects the size of a book. Which variable can be continuous?
a. number of pages
c. number of words
b. vertical space between lines
d. type of binding used
____ 83. An agricultural researcher wishes to study how the price of a new type of crop being grown in 10 counties
across the country will vary with the weather. What type of study will be the most appropriate?
a. cross-sectional study that uses a sample of the counties where the crop is grown
b. cross-sectional study that takes a census of the counties where the crop is grown
c. longitudinal study that uses a sample of the counties where the crop is grown
d. longitudinal study that takes a census of the counties where the crop is grown
____ 84. In which scenario is it better to take a sample rather than a census?
a. testing light bulbs being manufactured in a plant to see how long they last
b. determining the termite population in a city
c. both a and b
d. neither a nor b
19
Name: ________________________
ID: A
____ 85. A hospital study of 250 patients who underwent heart bypass surgery recorded the following for each patient:
age, gender, blood pressure, and number of heart attacks previously suffered. How many variables were
recorded altogether?
c. 254
a. 250
b. 1000
d. 4
____ 86. A study of 250 patients who underwent heart bypass surgery at a hospital recorded the following for each
patient: age, gender, blood pressure, and number of heart attacks previously suffered. The number of variables
measured that must be discrete is:
a. 0
c. 2
b. 1
d. 3
____ 87. Which of the following variables about a meal is qualitative?
a. calories
c. food groups represented
b. number of vegetable servings
d. preparation time
____ 88. A hospital administrator wants to know the length of wait in emergency rooms. The administrator also wants to
know whether age and seriousness of complaint affect the waiting time. For each patient treated in a 24-h
period, the emergency room staff records wait time in hours and if the patient is under age 18, 18–64 years old,
or age 65 or older. The staff also records if the patient was admitted to hospital. Which is true about this study?
a. longitudinal study with one quantitative variable and two qualitative variables recorded
b. longitudinal study with two quantitative variables and one qualitative variable recorded
c. cross-sectional study with one quantitative variable and two qualitative variables recorded
d. cross-sectional study with two quantitative variables and one qualitative variable recorded
____ 89. For the following thesis question, which type of study is the most appropriate? Do the grades of student athletes
across Canada change over the course of the school year?
a. cross-sectional sample
c. longitudinal sample
b. cross-sectional census
d. longitudinal census
____ 90. A survey of the driving habits for commuters asks the following questions:
How many people travel to work or school each day in your primary vehicle?
What distance do you commute to work or school?
How many vehicles do you own?
What did you pay in repairs last year?
What is true about the variables measured?
a. some are quantitative and some are qualitative
b. all are continuous
c. some are discrete and some are continuous
d. all are qualitative
20
Name: ________________________
ID: A
____ 91. A family wins two tickets to a concert. There are four people in the family: two parents and two children. In
order to decide who will attend the concert, the parents flip a coin to select which parent will attend. Then the
children flip a coin to select which child will attend. This selection method is an example of:
c. multi-stage random sampling
a. a simple random sample of size two
b. stratified random sampling
d. systematic random sampling
____ 92. The administration of a secondary school wants to collect student opinions on a proposed new timetable. They
decide to interview a simple random sample of 50 students in grade 9, a simple random sample of 50 students
in grade 10, a simple random sample of 50 students in grade 11, and a simple random sample of 50 students in
grade 12. This is an example of:
a. systematic random sampling
c. multi-stage random sampling
b. stratified random sampling
d. cluster random sampling
____ 93. A medical researcher wants to compare blood pressure readings between men and women in Toronto. She sets
up a station in a drug store and invites customers to have their blood pressure taken. She collects readings from
75 women and 47 men in one day. This is an example of:
a. a simple random sample since the researcher did not know beforehand who would
participate
b. a stratified random sample of men and women
c. a stratified random sample of people with high and low blood pressure
d. none of the above
____ 94. An airline wants to determine customer satisfaction with security measures being taken on its flights. The
airline randomly chooses 5 of its flights leaving from a randomly chosen airport. It asks all passengers on these
flights to complete a survey. This selection method is:
a. cluster random sampling
b. multi-stage random sampling
c. a combination of cluster and multi-stage random sampling
d. neither cluster nor multi-stage random sampling
____ 95. A city is interested in collecting opinions about its transit service from both users and non-users. It hires a
pollster who divides the city into blocks. The pollster then conducts a survey of the person answering at the
second house to the west of the northeast corner of each block. If the house is divided into apartments, the first
apartment on the ground floor is surveyed. The selected location of the house or apartment on each block is
randomly chosen. The sampling method used is:
a. simple random sample
c. stratified random sample
b. systematic random sample
d. cluster random sample
____ 96. Which of the following factors is not a consideration in determining the number of people to be interviewed in a
opinion survey?
a. whether the sampling method is simple random sampling or stratified sampling
b. how much variability exists in the opinions of the population
c. the number and variability of topics of the questions to be asked
d. the hope that the results are accurate to within 3% of the population values
____ 97. In order to determine the percentage of firecrackers that are duds, the manufacturer fires off every 1000th
firecracker produced. This is an example of:
a. destructive sampling
c. stratified sampling
b. simple random sampling
d. destructive stratified sampling
21
Name: ________________________
ID: A
____ 98. A survey was conducted of 1000 first-year university students across Canada. From all universities in Canada,
10 were randomly selected. Then at each of the selected universities, a random sample of 100 first-year
students were chosen to participate. This is an example of:
c. stratified random sampling
a. multi-stage random sampling
b. cluster random sampling
d. systematic random sampling
____ 99. A large university has 30 student residences. Each residence has 6 floors. In order to collect information about
students living in residence, the university selects 10 floors from the 180. Then it interviews everyone on those
floors. This is an example of:
a. multi-stage random sampling
c. cluster random sampling
b. stratified random sampling
d. systematic random sampling
____ 100. In a secondary school, there are 5 classes of grade 9 academic mathematics. The classes are labelled A, B, C,
D, and E. Each class has 30 students. In each class, the students are numbered from 1 to 30. The label A06
indicates the sixth student in class A. A random sample of 10 students enrolled in grade 9 academic
mathematics at this school results in the following students being selected:
A05,
A20,
B05,
B20,
C05,
C20,
D05,
D20,
E05,
E20
Which sampling method could not have been used?
a. simple random sampling
c. cluster sampling
b. stratified sampling
d. systematic random sampling
____ 101. In a secondary school, there are 5 classes of grade 9 academic mathematics. The classes are labelled A, B, C,
D, and E. Each class has 30 students. In each class, the students are numbered from 1 to 30. The label A06
indicates the sixth student in class A. A random sample of 10 students enrolled in grade 9 academic
mathematics at this school results in the following students being selected:
A09,
B13,
B15,
B24,
D11,
D12,
Which sampling method might have been used?
a. cluster random sampling
c.
b. systematic random sampling
d.
E02,
E13,
E18
stratified random sampling
none of the above
____ 102. In a secondary school, there are 5 classes of grade 9 academic mathematics. The classes are labelled A, B, C,
D, and E. Each class has 30 students. In each class, the students are numbered from 1 to 30. The label A06
indicates the sixth student in class A. A random sample of 10 students enrolled in grade 9 academic
mathematics at this school results in the following students being selected:
A01,
A03,
A09,
A12,
A19,
A21,
Which sampling method might have been used?
a. simple random sampling
b. multi-stage random sampling
c. either simple or multi-stage random sampling
d. neither simple nor multi-stage random sampling
22
A23,
A24,
A29,
A30
Name: ________________________
ID: A
____ 103. In a secondary school, there are 5 classes of grade 9 academic mathematics. The classes are labelled A, B, C,
D, and E. Each class has 30 students. In each class, the students are numbered from 1 to 30. The label A06
indicates the sixth student in class A. What sampling method will ensure that, in a sample of 10 students, there
is at least one student from each class?
a. simple random sampling
b. systematic random sampling of every 15th student where students are ordered by number
within the class
c. cluster random sampling
d. none of the above
An elementary school teacher is interested in assessing how students’ performance varies with the month of the
year in which they were born. In a sample of 500 grade 4 students, the birth months were distributed as follows.
Birth Month
Number of Students
January
31
February
24
March
40
April
45
May
50
June
44
July
35
August
43
September
53
October
41
November
49
December
45
____ 104. In a sample of 25 students, she has 5 born in January, 3 born in February, 4 born in March, 4 born in October,
5 born in November, and 6 born in December. What sampling method must not have been used?
a. simple random sampling
c. multi-stage random sampling
b. cluster random sampling
d. stratified random sampling
____ 105. Which sampling method will ensure that the teacher has students born in each month in the sample?
a. simple random sampling
b. cluster random sampling
c. systematic sampling where every 25th child is selected after the children are ordered by
birthdate
d. stratified random sampling
23
Name: ________________________
ID: A
____ 106. Which of the following behaviours by the person conducting a survey will not result in biased results?
a. The surveyor rewords questions for respondents who left questions blank in case they did
not understand the question.
b. The surveyor leaves the response to some questions blank if the respondent does not seem
to understand the question.
c. The surveyor fills in unanswered questions based on the responses to other questions.
d. The interviewer suggests possible answers to open-ended questions.
____ 107. Which of the following scenarios will not result in sampling bias?
a. The regular meeting time of a new group is determined by people who come to a Monday
afternoon meeting.
b. American food preferences are determined by a random sample of California residents.
c. Gas price fluctuations in a city are followed by taking a random sample of gas stations in
the city each Friday for a year.
d. none of the above
____ 108. Identify the type of bias that may be present in a telephone survey of a simple random sample of a city’s
residents to determine their opinions on city services.
a. household bias
c. neither a nor b
b. non-response bias
d. both a and b
____ 109. A famous poll was conducted by the magazine Literary Digest in 1936. In this poll, the presidential election
results were estimated from the responses of 2.3 million Americans. These people responded to a questionnaire
mailed to 10 million individuals who owned cars or telephones or subscribed to magazines. They tended to be
wealthier than the American population as a whole. How might the results be biased?
a. over-estimate of the number of people voting Republican since higher-income Americans
tend to vote Republican
b. under-estimate of the number of people voting Republican since higher-income Americans
tend to vote Republican
c. biased but will not affect the result because so many people responded
d. the results are not biased
____ 110. A grocery store wants to survey a large proportion of its customers. It leaves questionnaires in shopping bags
and asks people to return them to the store. In order to encourage a large response rate, respondents will be
entered into a draw for free groceries. What type of bias might exist by sampling shoppers this way?
a. not biased
c. non-response bias
b. sampling bias
d. response bias
____ 111. In a study of women's feelings about relationships, questionnaires were sent to 10 million American women.
More than 2.3 million women responded. Of the married respondents, 65% had extra-marital relationships.
Which of the following best describes this estimate?
a. not biased
b. over-estimates the true percentage because of non-response bias
c. under-estimates the true percentage because of household bias
d. biased but will neither under-nor over-estimate the result because so many people
responded
24
Name: ________________________
ID: A
____ 112. A police officer hides behind an overpass on an open stretch of highway and records the speeds of passing cars.
So that he can record speeds for all cars, he picks a time when the highway is not busy. Which of the following
will most likely describe the resulting estimate of the percentage of drivers who speed?
a. biased to give an estimate greater than the true percentage of speeders
b. biased to give an estimate smaller than the true percentage of speeders
c. unbiased
d. biased but not likely to either over or under-estimate the true percentage of speeders
____ 113. An airline conducts customer satisfaction surveys by having its passengers complete questionnaires on its
flights. In order to ensure that passengers have adequate time to complete the questionnaire, it is only given out
on overseas flights. What type of bias might result?
a. sampling bias
c. both a and b
b. non-response bias
d. it is not biased
____ 114. Which of the following scenarios is an example of response bias?
a. 100 surveys are given to voters; 20 are returned completed.
b. A member of parliament calls a sample of 100 of her constituents, introduces herself, and
asks how they will vote in the upcoming election.
c. 100 voters who live in two high-rise apartment buildings in a riding are asked how they
intend to vote.
d. Every 200th person on a voter's list for a riding is telephoned to find out how they will
vote.
____ 115. A magazine conducts an annual survey of its subscribers. One year it takes a random sample of 100 of its
subscribers and contacts them by telephone. If there is no answer, the subscriber is called back until a response
is obtained. The next year it puts a survey in all copies of the magazine. The survey is mailed to subscribers
and 1200 are completed and returned. Which of the following best describes the bias that results from these two
sampling methods?
a. the first is more biased since fewer people are surveyed
b. the first is less biased since it is based on a random sample
c. both methods suffer from bias
d. neither method will lead to biased results
____ 116. In order to determine the average cost of a minor operation in Ontario, the Ministry of Health samples Ontario
hospitals. In order to save costs, only hospitals in the Greater Toronto Area are surveyed. What best describes
the likely results of this survey?
a. not biased since most operations are performed in the Toronto area
b. affected by response bias
c. affected by sampling bias
d. affected by non-response bias
____ 117. A parents’ organization that tries to stop drunk driving wants to find out teenagers’ attitudes towards drinking
and driving. Parents from the organization visit each secondary school in a city at the time classes end for the
day. They interview the first 30 students leaving the building. What best describes the likely results of this
survey?
a. will suffer from response bias
b. will suffer from sampling bias
c. both a and b
d. not biased since students are interviewed from every school in the city
25
Name: ________________________
ID: A
____ 118. The vice-president of a school’s student council wishes to survey a sample of students for their opinion about
school dances. Which of the following methods will result in sampling bias?
a. Thirty of the vice-president’s friends and acquaintances, from across all grade levels, are
interviewed.
b. Thirty students, chosen randomly from all students who have the same lunch period as the
vice-president are interviewed.
c. neither a nor b
d. both a and b
____ 119. Which of the following is most true about telephone surveys?
a. always biased
b. never biased
c. not biased if participants are called at various times throughout the day
d. only biased if the telephone numbers called are not randomly selected
____ 120. Which of the following is most true about mail-in surveys?
a. sometimes biased
b. never biased
c. always biased
d. not biased if a large sample is received that is a cross-section of the population
____ 121. Determine the number of arrangements for the word BOXCAR.
a. 21
c. 46 656
b. 720
d. none of the above
____ 122. Determine the number of arrangements for the word CANADA.
a. 720
c. 240
b. 21
d. 120
____ 123. Determine the number of three letter arrangements using the letters of the word METAPHOR.
a. 336
c. 512
b. 40 320
d. 56
____ 124. Determine the number of ways that a prime minister, secretary, treasurer, and publicity minister could be
chosen from an art club of 12 members.
a. 495
c. 11 880
b. 48
d. 20 736
____ 125. Determine the number of ways you could line up 3 orange marbles, 5 blue marbles, and 1 purple marble.
a. 504
c. 24 192
b. 362 880
d. 15
____ 126. A bag contains 3 red blocks, 2 green blocks, and 4 blue blocks. Determine how many ways that all of them can
be drawn, one at a time, without replacement.
a. 362 880
c. 1260
b. 15 120
d. none of the above
26
Name: ________________________
ID: A
____ 127. Determine the number of ways the 8 members of the Junior Jazz Band can stand in a line if Val must be first,
Tim sixth, and Tricia last.
a. 56
c. 32 768
b. 40 230
d. none of the above
____ 128. Determine the number of ways that the 12 members of the boys' baseball team can be lined up if Joe, Tanner,
and Josh must all be together.
a. 220
c. 604 800
b. 362 880
d. 1 209 600
____ 129. A person buys a ticket for a draw which has tickets made up of four digits from 0 to 9, and one winning ticket
is drawn. Assuming that all the tickets have been sold, determine the probability of the person winning the
draw.
1
1
a.
c.
3024
10 000
1
1
b.
d.
5040
6561
____ 130. Express 15 × 14 × 13 in a different manner.
a.
b.
P(15, 13)
15!
2!13!
c.
d.
15!
12!
P(15, 12)
____ 131. The 7 members of a chess club line up for a picture. Determine the probability that Mckenzie and Johann will
be beside each other.
1
1
a.
c.
7
3
2
1
b.
d.
7
6
____ 132. A captain and co-captain for a fencing team are chosen from a hat with the names of all 11 members in the hat.
Determine the probability that Lauren and Isabel are chosen as captain and co-captain respectively.
1
1
a.
c.
110
55
1
2
b.
d.
121
121
____ 133. The letters of the word SIMILE are scrambled. Determine the probability that the word is spelled exactly
backwards.
1
1
a.
c.
720
6
1
b.
d. none of the above
360
27
Name: ________________________
ID: A
____ 134. The letters of the word CHEMISTRY are put in a hat and three letters are drawn, one at a time, without
replacement. Determine the probability that the C and R are chosen.
1
1
a.
c.
252
24
14
1
b.
d.
243
12
____ 135. The face cards of a deck are shuffled and two cards are drawn, one at a time, without replacement. Determine
the probability that both cards are diamonds.
1
1
a.
c.
132
24
1
b.
d. none of the above
66
Short Answer
136. Tung studies the types of vehicles driving by his house and records the results in a table.
Type
Frequency
Car
12
Minivan
10
Sport Utility
6
Pickup
6
Truck / Van
4
Other
2
Tung wants to create a circle graph to represent the data. Determine the measure of the sector angle for the
Pickup category.
137. Tom measured the heights, in centimetres, of 30 corn plants and created the following stem-and-leaf plot.
Stem
Leaf
15
2245
16
113478
17
0112356889
18
12268
19
458
20
23
Determine the median of the heights.
28
Name: ________________________
ID: A
138. Students at a high school were asked how they travel to school each day. The results are summarized in the
following circle graph.
If 208 students take the bus, determine the number of students who walk to school.
139. The following circle graph represents data from 1500 people. The sector angle for category A is 54°. Determine
the frequency of category A.
140. State the value of P(15, 3).
141. Express 40 × 39 × 38 using factorials.
142. Evaluate
100!
96!3!2!
.
143. State the number of words that can be formed by rearranging the letters of the word PROBABILITY.
144. State the number of ways that a committee of a president, treasurer, and secretary can be selected from a
students' council with 15 members.
145.
State the number of ways that the 9 members of the debating club can be lined up for a picture if Frasier must
be on the far left and Samantha and Charlotte must be together.
146. Solve for n if
n!
(n − 1)!
= 42.
147. Four identical chocolate bars, three identical bags of chips, and 6 identical popsicles are lined up on a prize
table. Determine the number of ways that this could be done.
29
ID: A
Sample Mastery Questions Test 1
Answer Section
MULTIPLE CHOICE
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ID: A
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C
D
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ID: A
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D
C
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B
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B
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A
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D
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B
B
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D
A
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A
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3
ID: A
127.
128.
129.
130.
131.
132.
133.
134.
135.
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C
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B
A
B
D
D
SHORT ANSWER
136. ANS:
Frequency for the Pickup category is 6.
The sum of all frequencies is 40.
6
× 360° = 54°
The sector angle for the category is
40
137. ANS:
Since there are 30 data values, the median will be the average of the 15th and 16th data values.
173 + 175 348
Median =
=
= 174
2
2
Therefore, the median height is 174 cm.
138. ANS:
Let x represent the number of students who walk to school.
48
x
=
208 26
x = 384
Therefore, 384 students walk to school.
139. ANS:
54°
Percentage in category A =
× 100% = 15%
360°
Frequency of category A = 0.15 × 1500 = 225
The frequency of category A is 225 people.
140. ANS:
The value of P(15, 3) is 2730.
141. ANS:
40!
Using factorials, 40 × 39 × 38 is
.
37!
4
ID: A
142. ANS:
When
100!
96!3!2!
is evaluated, it equals 3 921 225.
143. ANS:
The number of words that can be formed is 9 979 200.
144. ANS:
The number of ways that a committee of a president, treasurer, and secretary can be chosen is 2730.
145. ANS:
The number of ways is 10 080.
146. ANS:
n = 42
147. ANS:
The number of ways that this could be done is 60 060.
5