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:

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.

Q2:

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.

Q3:

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.

Q4:

Elizabeth is doing a research project on whether or not students in her school eat healthy food. She decides to interview her friends who do gymnastics with her. Is her sample biased?

  • ANo
  • BYes

Q5:

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

Q6:

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

Q7:

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

Q8:

A student wants to research the number of students in his middle school who ride the school bus. Which of the following is the best method to obtain an unbiased sample?

  • AAsking all of the students in the library on Thursday if they ride the school bus
  • BAsking a random sample of 100 students during lunchtime if they ride the school bus
  • CAsking a random sample of 50 students from his grade if they ride the school bus
  • DAsking all of the students in the gymnastics team if they ride the school bus
  • EAsking a random sample of 5 students in the hallway if they ride the school bus

Q9:

A restaurant owner wants to conduct a survey about whether the residents of a town prefer his restaurant over others or not. His plan is to ask a random sample of the restaurant customers to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased?

  • AThe restaurant customers will not want to spend time filling in the questionnaire.
  • BThe number of customers in the chosen sample is not large enough.
  • CThe restaurant customers are likely to prefer his restaurant.
  • DWe do not know how he will ensure that the sample is random.

Q10:

The government wants to conduct a survey about the number of people in a town who think that a park needs to be remodeled. Their plan is to ask a random sample of the park’s visitors to fill in a questionnaire. Which of the following would most likely be the reason the sample is biased?

  • AThe park visitors would be more interested in remodeling the park.
  • BThe number of visitors in the chosen sample is not large enough.
  • 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.
  • EThe visitors will not want to spend time filling in the questionnaire.

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