Bias in Samples

Why do we randomly select our samples?

• for control

• reduce bias

• so we don't get the same answers from everyone

• to eliminate confounding results

At a middle school, the 7th graders will conduct a survey for where to go on a field trip. Which method will result in the least biased decision?

• to randomly ask 8th grade students who went on a field trip last year

• to randomly choose some 7th grade students to select a location

• to ask all 7th grade teachers and administrators for a location

• to ask the student council to choose a location

This target depicts what?

• Low bias, low variability

• High bias, low variability

• Low bias, high variability

• High bias, high variability

Why do we want our samples to be random?

• To decrease the margin of error

• To increase our confidence

• To decrease variability

• To decrease bias

Tanya wants to know the percent of people likely to attend the upcoming musical at school. She asks each person in the musical how many people they know who are coming to make a prediction. Why is this sample biased?

• Drama students are more likely to lie.

• Musicals are better attended than plays.

• The drama teacher was not asked.

• The sample is not random and not representative of the entire school population.

Answer explanation

The sample is not random and not representative of the entire school population, as it only includes people involved in the musical, leading to bias.

In order to estimate the proportion of students that text while driving, a school administrator selects a simple random sample of students from a list of all students at the school who have parking permits. The students are called to the office, one at a time. The administrator asks each student, “Do you text while driving, even though you are not supposed to?” Based on the survey, the administrator estimates that only 2% of students with parking passes text while driving. What potential bias is present in the design of this survey and what is the likely direction of the bias?

• The sample proportion is likely an underestimate of the population proportion due to response bias.

• The sample proportion is likely an underestimate of the population proportion due to undercoverage.

• The sample proportion is likely an underestimate of the population proportion due to nonresponse.

• The sample proportion is likely an overestimate of the population proportion due to response bias.

• The sample proportion is likely an overestimate of the population proportion due to undercoverage.

In a certain school, students can choose whether to eat in the school’s cafeteria. A reporter working for the school’s newspaper polled students on their reactions to changes in the menu at the cafeteria. For each student leaving the cafeteria in one 20-minute time period, the reporter used a die to determine whether to stop the student and ask how he or she felt about the new menu. In the reporter’s article it was stated that a random sample of the students showed that 23% of the school’s student population was happy with the new menu. Which of the following statements is true?

• Because each student leaving the cafeteria was randomly selected and could choose to answer or not, this is a random sample of the student population, and the 23% is an accurate measurement of the school population’s view of the new menu.

• Because students self-selected whether to eat in the cafeteria, the sampling method might be biased and the sample might not be representative of all students in the school.

• The survey would have been more effective if the reporter had collected the data in one 10-minute time period rather than in one 20-minute time period.

• The survey would have been more effective if students who cared about the food could have called the reporter to tell how they felt about the new menu, so that only students with opinions on the subject would have been surveyed.

• Because no treatment was imposed on the students eating in the cafeteria, one cannot make any conclusions about the new menu.

A student wants to know which type of pizza the students at his high school prefer. Which option would give an unbiased sample?

• Asking all the students in the hot lunch line.

• Asking 10 students from each homeroom

• Asking 100 random students, chosen by drawing names from a hat

• Asking all the 10th graders

This target depicts

• High bias, high variability

• High bias, low variability

• Low bias, low variability

• Low bias, high variability

Poll on women’s issues interviewed 1025 women randomly selected from the United States. One question was “Many women have better jobs and more opportunities than they did 20 years ago. Do you think women had to give up too much in the process, or not?” Forty-eight percent of women in the sample said “Yes.” Why can't we just say that 48% of women felt they gave up too much?

• Not all samples would result in 48%

• The margin of error might change.

• The confidence interval might change

• This was a biased survey.