AP Statistics Sampling Types and Bias

How do random sampling and stratified sampling differ from each other?

• Random sampling involves giving each member of the population an equal chance of being selected, while stratified sampling involves dividing the population into homogeneous groups and taking a random sample from each group.

• Random sampling involves dividing the population into homogeneous groups and taking a random sample from each group, while stratified sampling involves giving each member of the population an equal chance of being selected.

• Random sampling involves selecting each member of the population based on a specific characteristic, while stratified sampling involves giving each member of the population an equal chance of being selected.

• Random sampling involves dividing the population into heterogeneous groups and taking a random sample from each group, while stratified sampling involves selecting each member of the population based on a specific characteristic.

Can you differentiate between systematic sampling and cluster sampling?

• Systematic sampling involves selecting a random sample of individuals from each cluster in the population.

• Cluster sampling involves selecting every nth element in a population.

• Systematic sampling involves selecting every nth element in a population, while cluster sampling involves randomly selecting clusters and including all individuals within those clusters in the sample.

• Cluster sampling involves randomly selecting clusters and including all individuals within those clusters in the sample, while systematic sampling involves selecting every nth element in a population.

Identify the sampling method:

Every fifth person boarding a plane is searched thoroughly.

• SRS

• Stratified

• Cluster

• Systematic

• Voluntary Response

Identify the sampling method:

At a local community College, five math classes are randomly selected out of 20 and all of the students from each class are interviewed.

• SRS

• Stratified

• Cluster

• Systematic

• Convenience

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

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.

The School Dance Committee conducts a survey to find what type of music students would like to hear at the next dance. Which sampling method is least likely to result in a biased sample?

• Call the top 20% of the senior class. 

• Interview every 10^th student as they enter the school.

• Ask every 5^th person leaving a school jazz band concert.

• Set up a hip-hop only website where students can list their 3 favorite songs if they open up the link.

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 sample should be

• representative of  only middle school students only

• a very large group

• representative of the population

• representative of people who volunteer

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