Statistics: Designing a Survey: Question Bias and Sampling Worksheet

Question 1

A school wants to know which lunch option students prefer. The survey question says, "Do you agree that the delicious new pasta should be served more often?" Explain why this question may be biased and rewrite it to be more fair.

Accepted Answer

The question is biased because the word "delicious" pushes students toward a positive answer. A fairer question is, "Which lunch option would you like served more often: pasta, tacos, salad, sandwiches, or another option?"

Question 2

A student asks only members of the basketball team whether the school should buy new basketballs. What is the population of interest, what is the sample, and why might the sample be biased?

Accepted Answer

The population of interest is the group the student wants information about, such as all students at the school. The sample is only the basketball team members. The sample may be biased because basketball players are more likely than other students to support buying new basketballs.

Question 3

The table shows how 80 students were surveyed about a new homework policy. Identify whether the sample seems representative of the whole school and explain your reasoning. Grade 6: 60 students surveyed, Grade 7: 10 students surveyed, Grade 8: 10 students surveyed.

Accepted Answer

The sample does not seem very representative because Grade 6 students make up most of the sample. A better sample would include a more balanced number of students from each grade, or a number from each grade that matches the school's actual grade sizes.

Question 4

Rewrite this survey question so it is not biased: "Don't you think our school should stop wasting money on field trips?"

Accepted Answer

A fair version is, "Do you think the school should continue spending money on field trips, reduce spending on field trips, or stop spending money on field trips?" This wording avoids calling field trips a waste of money.

Question 5

A city wants to know how residents feel about building a new park. Which sampling plan is likely to be least biased? A: Ask people entering a sporting goods store. B: Ask every 20th person from a list of all city residents. C: Ask only people who live next to the proposed park. D: Post an online poll and count anyone who chooses to answer.

Accepted Answer

Plan B is likely to be least biased because it uses a systematic sample from a list of all city residents. The other plans are more likely to overrepresent people with certain interests or strong opinions.

Question 6

A website poll asks, "Should the school finally make the obvious choice and start later in the morning?" It receives 500 responses. Name two problems with using this poll to decide the school schedule.

Accepted Answer

One problem is that the wording is biased because it says starting later is the obvious choice. Another problem is that the poll is voluntary, so people with strong opinions may be more likely to answer than other students or families.

Question 7

A teacher wants to estimate the average number of minutes students spend reading each night. The teacher randomly selects 5 students from each homeroom. What type of sampling method is this, and why might it be useful?

Accepted Answer

This is a stratified sampling method because students are grouped by homeroom and a random sample is taken from each group. It is useful because every homeroom is included in the sample.

Question 8

A survey asks, "How many hours of video games do you waste each week?" Explain the bias in the question and write a fair version.

Accepted Answer

The question is biased because the word "waste" makes playing video games sound negative. A fair version is, "How many hours do you spend playing video games each week?"

Question 9

A principal surveys the first 40 students who arrive at school on Monday to learn whether students want more morning clubs. Explain why this sample could be biased.

Accepted Answer

This sample could be biased because students who arrive early may be more interested in morning activities than students who arrive later. The sample may not represent all students at the school.

Question 10

A school has 600 students: 200 in Grade 6, 200 in Grade 7, and 200 in Grade 8. You want a random sample of 60 students that is balanced by grade. How many students should be chosen from each grade? Explain your method.

Accepted Answer

The sample should include 20 students from each grade. Since the school has equal numbers of students in Grade 6, Grade 7, and Grade 8, the 60-person sample should be split equally among the three grades.

Question 11

Decide whether this is a good survey question and explain your answer: "Which school subject do you like best: math, science, language arts, or social studies?"

Accepted Answer

This is a fairly clear survey question, but it may be improved by adding an "other" choice or listing all subjects offered at the school. Without those choices, some students may not be able to answer accurately.

Question 12

A student wants to find out what snacks middle school students prefer. Design a short survey plan that includes a fair question and a sampling method that is likely to reduce bias.

Accepted Answer

A fair question is, "Which snack would you most like to have available at school: fruit, granola bars, popcorn, crackers, yogurt, or another snack?" A good sampling method is to randomly select students from each grade level so that Grade 6, Grade 7, and Grade 8 students are all represented.

Statistics: Designing a Survey: Question Bias and Sampling

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