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6. The heights of ten buildings in a city, in feet, are shown.
102 54 76 95 250 37 65 48 27 85
For each data set, use your calculator or the random digit table below to generate four random numbers between 1 and 10. Then use the numbers you generated to create a random sample of four from the data set.
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12. A coach records the heights of players on her softball team, in meters.
Player 1 2 3 4 5 6 7 8 9 10
Height 1.8 1.5 1.6 1.6 2.2 1.3 1.7 1.8 2.0 2.1
In Exercises 13 through 18, use the given data set to create a stratified random sample of the specified size. Explain the criteria by which you selected your sample.
13. The data set below shows the highest temperature recorded for select cities on
different continents.
Highest Temperature Recorded
North America Europe Asia Africa
81 95 94 101
92 81 86 96
90 102 92 103
104 98 97 94
87 87 107 98
111 103 91 107
76 92 102 97
94 97 97 98
95 100 93 112
89 96 88 96
a. Create a stratified random sample of 4 temperatures.
Sample answer: {81, 103, 97, 98}; I randomly chose one temperature from each of the four continents.
b. Create a stratified random sample of 8 temperatures.
Determine the type of sampling technique being used in each situation. Choose from simple random sampling, cluster sampling, stratified sampling, systematic sampling, subjective sampling, convenience sampling, or volunteer sampling.
25. A teacher chooses the first student in each row to do a math problem at the board.
systematic sampling
26. A physical education teacher chooses the five students with the best times in a
cross country event.
27. A principal randomly chooses eight student ID numbers to participate in a survey.
28. A teacher chooses students with their hands in the air to put problems on the board.
29. A principal chooses the first 12 students into the auditorium to help pass out programs.
30. A teacher chooses her favorite 8 problems from the lesson to demonstrate to the class.
Determine whether each study has a source of bias. If so, describe the bias and explain why the bias makes the sample unrepresentative.
31. A survey is mailed to voters in Albany asking “Will you vote for the sales tax
increase in Albany?”
There is no bias in this study.
32. A survey is mailed to voters in Albany who make more than $100,000 a year asking,
“Will you vote for the sales tax increase in Albany?”
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5. To determine if there is a link between the number of hours a student oversleeps
and student grades, a teacher asked 125 students to track the number of minutes
they oversleep each day for a month.
6. A medical researcher who wants to see if there is a link between the weight of a
patient and the patient’s blood pressure asks 100 doctors to track the weight and
blood pressure of one-half of their patients who are randomly chosen and answer
specific questions about each patient.
For each situation, identify the population, the sample, and the characteristic of interest.
7. A teacher wanted to know if students who study for more than two hours for a test
will get a better grade on the test than students who study for two hours or less.
She asks her students to log their study time for the test. She gathers data from
three classes taking the test.
The population is students. The sample is the students in three classes. The characteristic is the link between study time and performance on the test.
8. One hundred middle school math students are randomly divided into two groups,
one in which a 4-function calculator is used at all times and one in which a
4-function calculator is never used. The principal wants to determine if student
grades are higher if they can always use a calculator.
9. To determine if there is a link between environmental factors and cancer in women,
researchers examined the rate of cancer for 10,000 women who are sisters of
previous cancer patients. The researcher asked the women to respond to 50
questions about their environment as they were growing up.
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17. A band student parent group wants to conduct a survey to determine what percent
of parents are willing to sponsor the purchase of new instruments.
18. A school board wants to conduct a survey of city residents to see if they would
support a decrease in funding for sophomore sports.
Explain how confounding could have occurred for each observational study.
19. A teacher wanted to know if students who use graphing calculators use programs
to help them evaluate formulas. She asks her students whether they use graphing
calculator programs to evaluate formulas. She gathers data from three classes.
The concern is if students write their own programs as opposed to using professionally developed ones to evaluate formulas. If students write their own, they may not know the correct steps for evaluating formulas.
20. To determine if there is a link between eating breakfast and student grades, a
teacher asked 125 students to track the number of days each week for a month
that they eat breakfast before coming to school.
21. A parent-teacher group wants to see if there is a link between the occupation of a
parent and the level of participation in volunteer activities that the group sponsors. They
send a letter to parents of 300 random students in the school and ask them to list their
occupation and level of participation in volunteer activities sponsored by their group.
22. A study conducted by the owner of an art school wants to know if the total
enrollment in his weekday classes will increase if he drops the canvas fee.
23. A study used by a news agency wants to know if there is link between the income
level in a family and whether they have a parent in a nursing home.
24. A politician wants to see if there is a link between the income level of his
constituents and the amount of money they are willing to contribute to his campaign.
Identify the treatments in each experiment. Then determine how the differences in treatments can be analyzed and interpreted in order to draw a conclusion.
25. One hundred geometry students are randomly divided into 4 classes – one in which
a drawing program is used at all times to draw geometric shapes and one in which
a drawing program is never used. The department chair wants to determine if
students’ geometry grades are higher if they have to draw a geometric figure with a
drawing program.
There are two treatments. One uses a drawing program and the other does not. The differences in treatments were analyzed by recording the grades for specific tests that included analyzing geometric figures and then comparing the grades on the tests.
26. Sixty juniors are randomly chosen and divided into two groups – one in which
all students participate in an extra-curricular activity and the other in which no
students participate in an extra-curricular activity. The Student Council sponsor
wants to determine if student grades are higher at the end of the year if students
participated in an extra-curricular activity during the school year.
Name _____________________________________________ Date ____________________
Do It YourselfDesigning and Collecting Data Using a Survey, Study, or Experiment
Problem SetEach of the following questions is best answered by a survey, a study, or an experiment. Identify the best method to use. Then explain how you would obtain a random sample and why the technique you chose is appropriate.
1. You want to determine the average income of public school teachers in a certain city.
Answers will vary. Sample answer: a study. Assign each public school teacher an ID number and use a computer to randomly generate a sample of teachers. This technique provides a random sample of the population of teachers in the city, and random sampling is typically representative of a population.
2. You want to compare the average income of male and female public school
teachers in a certain city.
3. A company wants to determine whether their drugs are harmful to people in the
following age groups: 0–10, 11–21, 22–35, and 40 and above.
4. A company wants to determine whether their drugs are harmful to people in a
5. A university wants to study the economy of towns that have a heavy drug
presence, but they can only study three towns.
6. A local hospital wants to compare the effects of drugs on people in the age groups
14 –17 and 18 –23.
For each survey, observational study, or experiment, determine which of the following sampling techniques would be the most appropriate: random sampling, stratified random sampling, or clustered sampling. Then explain how you would obtain a sample and why the technique you chose is appropriate.
7. A newspaper wants to determine which areas of town have the least number of
subscriptions.
Sample answer: stratified random sampling; Divide the population of the town into groups according to their geographic location (possibly north, south, east, west), and randomly select members from each group. This technique provides a random sample from all areas of town. Random sampling is typically representative of a population.
8. You want to estimate the number of people in your school who are vegetarians.
9. You want to determine whether 9th graders or 11th graders are more likely to be
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Identify and explain any possible sources of bias in the given situation.
25. A cell phone company wants to know how many times adults typically use
text-messaging in one month. The company asks a random sample of adults
that subscribe to their cell phone service, “How many times did you text-message
last month?”
Answers will vary. Sample answer: The sample is biased because they only asked adults that use their cell phone service, and this may not be representative of the adult population using cell phones. It is also biased because “last month” may have been a month with an atypical volume of cell-phone usage.
26. A principal wants to know if students should be allowed to use cell phones while
in the classroom. She surveys one math class to see how many students have cell
phones and asks them how they could use their cell phones to improve instruction.
27. A principal wants to know if students should be allowed to use graphing calculators
in the classroom. She surveys one English class and asks, “How do you use a
graphing calculator to improve instruction?”
28. A teacher wants to know how students use graphing calculators while in the