Random and Bias 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

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.

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.

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

A tax preparation company wants to see how satisfied its customers are with their services. Which of the following would give them the best unbiased sample?

• looking at customer reviews on their social media page

• questioning the first 25 people that call the company

• asking the last 25 people on an alphabetical list of all of their current customers

• surveying a random sample of customers from a list of all of their current and previous customers

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.

Disneyland often surveys its guests as they exit a restaurant during their visit. The surveyor stands at the restaurant exit, counts the number of people leaving, and surveys every 25th guest.
This is a form of:

• Simple Random Sample

• Stratified Random Sample

• Voluntary Response

• Systematic Random Sampling

Identify the type of sampling used:

A teacher splits her classes up by period. She then uses a RNG to select 10 students from each period to participate in a survey.

• Stratified Random Sample

• Systematic Random Sample

• Cluster Random Sample

• Biased Sample