Lesson Worksheet: Biased versus Unbiased Samples Mathematics • 7th Grade
In this worksheet, we will practice distinguishing between systematic, self-selected, convenience, and stratified sampling and determining whether a sample is biased or unbiased.
Q1:
A school principal wants to find out what the students think about the teaching quality in the school. Which of these samples is unbiased?
- AA list of female students to interview is randomly generated.
- BA list of students to interview is randomly generated.
- CA questionnaire is available at the library for anyone who wants to take part in the survey.
- DA list of male students to interview is randomly generated.
- EAll ninth grade students are interviewed.
Q2:
An animal rescue center wants to find out if people in its town think more money should be spent on animal welfare. They plan to ask a random sample of their visitors and volunteers to fill in a questionnaire. Why would their sample not be representative of the town’s population?
- AThe center’s visitors and volunteers are likely to be supportive of spending on animal welfare.
- BPeople will not want to spend time filling in the questionnaire.
- CWe do not know how they will ensure that the sample is random.
- DThere might be a high proportion of children in the sample, which will skew the result.
Q3:
A teacher wanted the children in her class to have a random sample of coins for a lesson. She put nickels, quarters, and dimes into a bag, and the bag was passed around the class for each child to select a coin without looking in the bag. Why is this unlikely to produce a random sample of coins?
- AThe students might look in the bag and choose a coin that they have seen, so they will not be selecting the coin at random.
- BThe students might be able to identify the coins by feeling their size and weight, so they will not be selecting the coin at random.
Q4:
A student wants to research the amount of pocket money students in his middle school receive. Which of the following would be the best way to get a representative sample of the population?
- AAsking a random sample of 50 students from his grade how much pocket money they receive
- BAsking a random sample of 20 students from each grade how much pocket money they receive
- CAsking the teachers of each class how much pocket money they think the students in their class receive
- DAsking all of the students in the library on a Monday lunchtime how much pocket money they receive
Q5:
Which of the following is a representative sample?
- AA hospital wants to investigate the reasons why people go to the emergency room, so questionnaires are handed out to a random sample of people waiting in the emergency room on a Monday morning.
- BA market research company wants to find out how much waste people recycle, so they survey 100 people at the city recycling drop-off location.
- CA student wants to find out how much students at their school enjoy math classes, so they give a questionnaire to everyone at the math club.
- DTo find out how students travel to school, student representatives from each grade ask a random sample of 20 students from across their grade.
Q6:
A teacher wanted the children in her class to have a random sample of coins for a lesson. She put nickels, quarters, and dimes into a bag and passed it around the class for each child to select a coin without looking inside.
Why is this unlikely to produce a random sample of coins?
- AThe students might look in the bag and choose a coin that they have seen, so they will not be selecting the coin at random.
- BThe students might be able to identify the coins by feeling their size and weight, so they will not be selecting the coin at random.
- CThe bag might be transparent, so the students will see the coins and will not be selecting the coin at random.
Q7:
A fair coin is thrown randomly four times; it lands on heads every time.
Which of the following is true?
- AThe coin will land on heads next time because it lands on heads every time.
- BThe coin will land on tails next time because it has landed on heads so many times.
- CThe coin could land on heads or tails next time it is thrown because it is not affected by what has happened previously.
Q8:
Is choosing a marble from a jar an experiment?
- AYes
- BNo
Q9:
A coin is thrown randomly 50 times, falling heads up 32 times.
Which of the following is true?
- AThe coin will show heads next time because it shows more heads than tails.
- BThe coin will show tails next time because it has shown so many heads.
- CThe coin could show heads or tails next time it is thrown because it is not affected by what has happened previously.
Q11:
Liam wants to find out the proportion of seventh grade students who have already been abroad. There are 250 seventh grade students in his school. He decides to number all of them from 1 to 250, generate a random list of 40 numbers between 1 and 250, and then interview the corresponding students. Is his sample biased?
- ANo
- BYes
Q12:
A lamp manufacturer has two lines of fabrication, line 1 and line 2, and the work is organized in two eight-hour shifts. The quality manager plans to introduce new quality checks using new power measurement devices. They decide to measure the power of the lamps exiting line 1 between 10:00 and 10:15 am every day for one week. Is their sample biased?
- ANo
- BYes
Q13:
A doctor wants to find out about some possible side effects of a common drug they have prescribed. Which of these samples is unbiased?
- Asending a survey to a select group of their patients
- Binterviewing all the patients who come for an appointment on a Saturday
- Cinterviewing patients who come for an appointment during the week at random
- Dinterviewing patients who suffer from side effects of the drug
- Egenerating a list of patients to interview by phone randomly from the patient registry
Q14:
A church organization wants to poll citizens on their opinion of religious education in schools. They send a survey to all their members around the country. Is their sample biased?
- ANo
- BYes
Q15:
Which of the following survey questions is least biased?
- ADrinking sodas during a high-protein meal has been shown to decrease metabolic efficiency, which may prompt the body to store more fat. How often do you drink sodas during meals?
- BHow often do you manage to drink water rather than sodas during meals?
- CFor each of the beverages given, indicate how often you drink them during meals.
- DOn a scale from 1 to 10, how do you rate the frequency and quantity of sodas you drink during meals?
Q16:
Identify the source of bias in the question: “Do you believe the government should implement measures proposed by the opposition which would ensure that everyone in the country has access to good health care services?”
- Aquestion preface
- Btwo questions in one
- Cbiased wording (or leading question)
- Ddesire to please
Q17:
Which of the following survey questions is least biased?
- ADo you think our product would suit young children and teenagers?
- BHow would you rate our product on a scale from 1 to 10?
- CDo you love our product?
- DWhat do you love about our product?
Q18:
Which of the following survey questions is least biased?
- AMany studies show that gender differences are a societal construct. Do you believe that gender has an influence on children’s natural learning abilities?
- BDo you believe that girls are naturally better at foreign languages and schools should give them the possibility to learn more than two foreign languages?
- CDo you believe that boys are naturally better at maths than girls?
- DDo you like the philosophy of our school that girls and boys should be educated differently?
- EDoes gender have an influence on children’s natural learning abilities?
Q19:
What is the source of bias in the question “do you agree that recycling is important for the future of our planet?”
- Aquestion preface
- Bdesire to please
- Ctwo questions in one
Q20:
Which of the following survey questions is least biased?
- AAre nurses salaries too high, about right, or too low?
- BThere is a concern in the country about the nurse shortage. Do you think nurses should be paid more?
- CShould nurses be paid more?
- DDo you believe the salaries of nurses and surgeons are appropriate?
Q21:
What is the source of bias in the following question?
Many studies show that breastfeeding diminishes the risk of breast cancer and provides many health benefits to the baby. Are you considering breastfeeding your baby?
- Abiased wording (or leading question)
- Bquestion preface
- Ctwo questions in one
- Ddesire to please
Q22:
Identify the source of bias in the question: “How would you rate the comfort and durability of these bed linens?”
- Atwo questions in one
- Bquestion preface
- Cdesire to please
- Dbiased wording (or leading question)
Q23:
A student conducts a survey about the number of hours that the students in his school study per day. Which of the following is an unbiased sample?
- AA random sample taken from primary students
- BA random sample taken from secondary students
- CA random sample taken from his class
- DA random sample taken from the school students
- EA random sample taken from girls in the school
Q24:
True or False: A conclusion from a biased sample is as trustworthy as a conclusion from a truly random sample of the population being studied.
- ATrue
- BFalse
Q25:
The Egyptian government wishes to conduct a survey about the Egyptian people’s satisfaction with the government plan. Which of the following is an unbiased sample?
- AA random sample taken from Egyptian females
- BA random sample taken from Egyptian employees
- CA random sample taken from Cairo’s population
- DA random sample taken from the Egyptian people
- EA random sample taken from Egyptian males