13-7 Using Sampling to Predict
Identify each sample as biased or unbiased and describe its type. Explain your reasoning.
1. To determine how many students at a middle school bring their lunch from home, all the students on one school bus
are surveyed.
SOLUTION: This is a biased, convenience sample because only the students from one bus were surveyed. So, this sampling
method is not representative of the entire school. All the students on 1 school bus might come from the same
neighborhood/economic status.
2. To determine the theme for the homecoming dance, the homecoming committee surveys one classroom.
SOLUTION: This is a biased, convenience sample because only the students from one classroom were surveyed. So, this
sampling method is not representative of the entire school.
3. To determine shopping habits at a department store, one male and one female shopper are randomly selected and
surveyed from each of their 75 stores.
SOLUTION: This is an unbiased, stratified random sample. The shoppers are first divided into non-overlapping groups and then 1
male and 1 female is selected randomly from each group.
4. ANALYZE TABLES The theater group took a survey about the type of popcorn they should sell during plays.
They randomly surveyed 52 students at lunch. Their results are shown in the table. Is this sampling method valid? If
so, how many of the boxes of popcorn should be caramel if they order 600 boxes?
SOLUTION: This is a simple random sample since the students were randomly chosen during lunch. So, this sampling method will
produce a valid prediction.
The students survey results showed that
or of the students preferred caramel. So, the students should order
or 150 boxes of caramel flavored popcorn.
Identify each sample as biased or unbiased and describe its type. Explain your reasoning.
5. To determine whether a new university library would be useful, all students whose student ID number ends in 2 are
surveyed.
SOLUTION: This is an unbiased, simple random sample because the students are randomly selected from the entire population of
students.
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6. To determine the quality of cell phones coming off an assembly line, the manager chooses one cell phone every 20
minutes and checks it.
produce a valid prediction.
The students survey results showed that
or of the students preferred caramel. So, the students should order
13-7 Using or 150 boxes of caramel flavored popcorn.
Sampling to Predict
Identify each sample as biased or unbiased and describe its type. Explain your reasoning.
5. To determine whether a new university library would be useful, all students whose student ID number ends in 2 are
surveyed.
SOLUTION: This is an unbiased, simple random sample because the students are randomly selected from the entire population of
students.
6. To determine the quality of cell phones coming off an assembly line, the manager chooses one cell phone every 20
minutes and checks it.
SOLUTION: This is an unbiased, systematic random sample because the cell phones are selected according to a time interval.
7. To determine the popularity of a musician, a magazine asks teenagers to log on to their website and participate in the
survey.
SOLUTION: The sample is biased because it is a voluntary response survey. Only those teenagers who are interested in
participating in the survey are part of the sample.
8. To determine whether a candidate for governor is popular with the voters, 30% of citizens in each of the 254
counties are surveyed.
SOLUTION: This is an unbiased, stratified random sample because the population is first divided into the 254 counties, and then
30% of the citizens are surveyed from each of those counties.
9. ANALYZE GRAPHS A school committee wanted to find out if students will recycle at school. The committee
randomly surveyed 25% of the teenagers at a mall on a Saturday afternoon. The results are in the graph. Is this
sampling method valid? If so, about how many of the 576 students at the school will participate in the program?
SOLUTION: This sampling method is not valid because it will include students who do not attend your school. So, the results can
not lead to a reasonable conclusion.
10. HEALTH Seven of the 28 students in math class have the flu. Is this sampling of the students who have the flu
representative of the entire school? If so, how many of the 464 students who attend the school have the flu?
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No; this is a biased sample. The flu may have been passed more easily between students in that class, so more of
them may have the flu than compared to the entire school population.
SOLUTION: sampling
method isto
notPredict
valid because it will include students who do not attend your school. So, the results can
13-7This
Using
Sampling
not lead to a reasonable conclusion.
10. HEALTH Seven of the 28 students in math class have the flu. Is this sampling of the students who have the flu
representative of the entire school? If so, how many of the 464 students who attend the school have the flu?
SOLUTION: No; this is a biased sample. The flu may have been passed more easily between students in that class, so more of
them may have the flu than compared to the entire school population.
11. CONCERT As people leave a concert, every 10th person is surveyed. They are asked if they would buy a T-shirt.
One hundred forty of 800 people surveyed said yes. Is this sampling method valid? If so, how many people would
you expect to buy T-shirts at the next concert if 7000 attend? Explain your reasoning.
SOLUTION: Yes; this is a systematic random survey because the sample is selected according to a numerical interval.
The survey results showed that
or expect to buy T-shirts at the next concert is
of the people surveyed said yes. So, the number of people you would or 1225.
12. ANALYZE TABLES Every hour, twenty customers in a grocery store are randomly selected and surveyed on
their milk preference. The results are shown in the table. After reviewing the data, the store manager decided that
40% of his total milk stock should be low-fat milk. Is this a valid conclusion? If not, what information should the store
manager review to make a better conclusion?
Milk Preference
Milk
Number
skim
88
low-fat
92
whole
60
SOLUTION: No; The sample is unbiased, but preference does not necessarily indicate what will be bought. The store manager
should review sales receipts to determine what types of milk have actually been bought.
13. VIDEOS A video store is considering adding an international movie section. They randomly selected 300
customers, and 80 customers agree the international movie section is a good idea. Should the store add this section?
Explain.
SOLUTION: No; only 80 out of 300 customers agree, which is 27%. From this random survey, you can predict that only about
27% of the customers would like a foreign movie section, so the store should not add such an area.
14. FOOD Ellis is planning on opening a restaurant in his community. He is conducting a survey to determine what type
of food people in the community like.
a. Describe an unbiased population sample that Ellis could survey to get unbiased results.
b. Write two questions that Ellis could ask.
c. After the survey is completed, how could Ellis use the results of the survey to determine what types of food he should serve in his restaurant?
SOLUTION: a. Sample answer: He could survey one of every 10 people that exit the local grocery store.
b. Sample answers: What types of restaurants do you visit most often? What is your favorite type of food?
c. Sample answer: He could use the results to determine the type of food he serves or even the type of atmosphere people would like in the restaurant.
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15. CARNIVAL The student council is planning to have a school carnival.
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Explain.
SOLUTION: only 80
out of 300 customers
agree, which is 27%. From this random survey, you can predict that only about
13-7No;
Using
Sampling
to Predict
27% of the customers would like a foreign movie section, so the store should not add such an area.
14. FOOD Ellis is planning on opening a restaurant in his community. He is conducting a survey to determine what type
of food people in the community like.
a. Describe an unbiased population sample that Ellis could survey to get unbiased results.
b. Write two questions that Ellis could ask.
c. After the survey is completed, how could Ellis use the results of the survey to determine what types of food he should serve in his restaurant?
SOLUTION: a. Sample answer: He could survey one of every 10 people that exit the local grocery store.
b. Sample answers: What types of restaurants do you visit most often? What is your favorite type of food?
c. Sample answer: He could use the results to determine the type of food he serves or even the type of atmosphere people would like in the restaurant.
15. CARNIVAL The student council is planning to have a school carnival.
a. Describe an unbiased population sample they could survey to determine types of games and activities to have at the carnival.
b. Write three questions the student council could ask their sample population.
c. Describe how the student council could use the results of the survey to determine what types of games and activities should be included at the carnival.
SOLUTION: a. Sample answer: They could survey everyone in the school, including the students and staff.
b. Sample answer: What types of food should we offer at the carnival? How many and what types of games should
we offer? Would you attend the carnival?
c. Sample answer: Most importantly, the results could show whether or not they should have the carnival. After that, the results could show what types of food and games they should offer.
16. GAMES An online gaming site conducted a survey to determine the types of games people play online. The results
are shown in the circle graph.
a. If 2500 people participated in the study, how many of them would play arcade or board games?
b. An article said 30% of Americans play card games online. Is this statement valid? Explain your reasoning.
c. Describe how the study could have been conducted so that it represented all Americans and not just online eSolutions Manual - Powered by Cognero
gamers.
SOLUTION: Page 4
a. Sample answer: They could survey everyone in the school, including the students and staff.
b. Sample answer: What types of food should we offer at the carnival? How many and what types of games should
we offer? Would you attend the carnival?
Sample answer: Most importantly, the results could show whether or not they should have the carnival. After 13-7c.Using
Sampling to Predict
that, the results could show what types of food and games they should offer.
16. GAMES An online gaming site conducted a survey to determine the types of games people play online. The results
are shown in the circle graph.
a. If 2500 people participated in the study, how many of them would play arcade or board games?
b. An article said 30% of Americans play card games online. Is this statement valid? Explain your reasoning.
c. Describe how the study could have been conducted so that it represented all Americans and not just online gamers.
SOLUTION: a. According to the survey 9% play arcade games and 11% play board games. So 11% + 9% or 20% would play
either arcade or board games. If 2500 participated, then 0.20 • 2500 or 500 people would play either arcade or board
games.
b. No, this statement is not valid. The statement is not valid because the study only included people that played
games online. It isn’t 30% of Americans, it’s 30% of online gamers so it is not representative of all Americans.
c. Sample answer: The study could have been sent to 100,000 people from all over the United States. If most of
them respond, a result that is representative of the population could be produced.
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