Sampling Methods

Intro to Sampling Methods

AP Statistics

Randomness

To create a fair and accurate picture of what is happening in this world, we must ensure randomness. An outcome is random if we know the possible values are but not the particular order it may come.

Multiple Choice

A random outcome is one in which...

• There is a long term predictable pattern to the observed outcomes

• All outcomes are equally likely 

• Outcomes are haphazard or unpredictable in the long run

• We know which outcomes will occur ahead of time

Multiple Choice

Decide if the following outcome is random:
A friend asks you to quickly name a professional sports team.  Is the sports team named random?

• Yes

• No

Multiple Choice

Decide if the following outcome is random:
Names are selected out of a hat to decide roommates for a dormitory. Is your roommate for the year random?

• Yes

• No

Multiple Choice

Decide if the following outcome is random:
Flip a coin to decide who takes out the trash.
Is who takes out the trash random?

• Yes

• No

Simulation

We use simulation to mimic reality because using real data may not be feasible. A simulation uses random numbers to represent the outcome of real events.

Building a Simulation

• Identify the component to be repeated

• Explain how you will model the component's outcome

• Explain how you will combine the components to model a trial

• State clearly what the response variable is (the trial's outcome)

• Run several trials

• Collect and summarize the results of the trials.

• State your conclusion

Multiple Choice

Suppose 30% of cereal boxes contain a picture of LeBron James, 20% a picture of Steph Curry, and 50% a picture of Ben Simmons.  Which of the following digit assignments correctly models this situation?

• Let 1 = LeBron James; Let 2 = Steph Curry; Let 3 = Ben Simmons

• Let 0-3 = LeBron James; Let 4-5 = Steph Curry; Let 6-9 = Ben Simmons

• Let 1-3 = LeBron James; Let 4-5 = Steph Curry; Let 6-9 = Ben Simmons

• Let 0-2 = LeBron James; Let 3-4 = Steph Curry; Let 5-9 = Ben Simmons

Multiple Choice

Suppose we want to select two students at random for a committee from a high school class containing 25 students.  If we evaluate the following random numbers two at a time from left to right, which two "students" would be selected?
Suppose we code each student with a unique number from 01-25:
470324127901249348872357335207

• 47 & 23 
• 03 & 24
• 24 & 12
• 4 & 7

Multiple Choice

To randomly select 25 basketball players from the 300 players in the NBA, I would:

• Number the players from 01-25, read 3 digits at a time from a random table, discarding repeats and numbers over 25, and then stop when I reach 25.

• Number the players from 0-299, read 2 digits at a time from a random table, discarding repeats and numbers over 299, and stop when I reach 25.

• Number the players from 01-299, read 2 digits at a time from a random table, discarding repeats and numbers over 300, and stop when I reach 25.

• Number the players from 001-300, read 3 digits at a time from a random table, discarding repeats, 000 and numbers over 300, and stop when I reach 25.

Populations vs Samples

A population is the entire group that you want to draw conclusions about. A sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population. Obtaining information from an entire population is done by census, It is often time consuming, costly, impractical and nearly impossible. Therefore we examine a sample of the population to make inferences. The sample has to be randomly selected from the population and unbiased. Bias is overemphasizing or underemphasizing some characteristic of a population; it is the bane of sampling. We use several different sampling methods in an attempt to limit bias as much as possible.

Multiple Choice

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

Multiple Choice

A part of the population is called a ________________.

• biased sample

• random sample

• sample

• convenience sample

Good Sampling Methods

In a statistical study, sampling methods refer to how we select members from the population to be in the study. If a sample isn't randomly selected, it will probably be biased in some way and the data may not be representative of the population.

There are many ways to select a sample—some good and some bad. Good sampling methods eliminate bias. Examples of good sampling methods are simple random sampling (SRS), stratified sampling, cluster sampling, and systematic sampling.

Multiple Choice

A teacher splits her classes up by period. She then randomly picks 3 students from each period to do a survey.

• Stratified.

• Systematic

• Cluster

• Biased.

Multiple Choice

A teacher wants to know how well her students are doing on a topic. She randomly picks one class to survey.

• Simple Random

• Cluster

• Stratified

• Systematic

Multiple Choice

A teacher hands out an index card and asks ALL of her students to write down the following information: age, height (in inches), and what grade they are in.

Which of the following best describes her method of data collection?

• Census

• Simple Random Sample

• Cluster Random Sample

• Stratified Random Sample

Multiple Choice

An independent research company wants to go door to door to survey people in the city of Fontana. The company decides to number all blocks within the city limit, randomly choose 1 block and survey all households on that block.

This is an example of:

• Simple Random Sample

• Stratified Random Sample

• Cluster Random Sample

• Systematic Random Sampling

Multiple Choice

A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.

She picks the student in every 5th seat.

• Simple Random

• Systematic

• voluntary response

• convenience

Multiple Choice

A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.

She selects the five closest to her desk.

• simple random

• Self Selected.

• Convenience

• Systematic Random

Multiple Choice

A teacher wants to know the average time spent doing homework by the students in her class of 20 girls and 5 boys.

She selects the first five who raise their hands.

• Systematic

• Convenience

• Self Selected

• Simple Random

Multiple Choice

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

Multiple Choice

Marianne wanted to know students' opinion on the new schedule at school. She survey's the first 30 students who come into her class.

• Convenience Sampling

• Systematic Random Sampling

• Simple Random Sampling

• Volunteer response

Multiple Choice

Political webpages often allow readers to rate (if they want to) whether they strongly agree, agree, disagree, or strongly disagree with the President's decision on any given situation. This is a form of:

• Self-Selected

• Convenience Sampling

• Simple Random Sampling

• Systematic Random Sampling

Multiple Choice

Interview every 10th student who enters the school in the morning.

• simple random

• voluntary response

• systematic

• convenience

Biased Sampling

A sampling method is called biased if it systematically favors some outcomes over others. There are different types of bias. response bias (the wording of questions will elicit a favored response), undercoverage (part of the population is not represented), non-response bias (a large fraction of those sampled fail to respond occurs when a subject can choose to participate, and voluntary response bias (individuals can choose whether or not to participate).

Bad sampling methods are convenience and voluntary response sampling

Multiple Choice

A nonsampling error occurs when someone gives an incorrect response to a sample survey. What is it called when a systematic pattern of incorrect responses occurs?

• nonresponse

• bias

• response bias

• undercoverage

Multiple Choice

I want a representative sample of likely voters. I use a telephone directory to randomly select 200 people. What is the most apparent bias?

• Undercoverage

• Nonresponse

• Response

• Voluntary Response

Multiple Choice

Many websites like Amazon and Yelp include customer ratings and reviews of products, restaurants, hotels, and so on. What is the predominant bias evident in these ratings and reviews?

• Response Bias

• Non-Response Bias

• Undercoverage Bias

• Voluntary Response Bias

Multiple Choice

“Some cell phone users have developed brain cancer. Should all cell phones come with a warning label explaining the danger of using cell phones?”

What kind of bias is evident in this survey question?

• Undercoverage Bias

• Non-Response Bias

• Response Bias

• Voluntary Response Bias

Multiple Choice

Source of bias in which people CHOOSE to respond and usually only people with very strong opinions respond

• Response Bias

• Undercoverage

• Convenience Sampling

• Voluntary Response

Multiple Choice

Source of bias in which some groups of populations are LEFT OUT of the selection process

• Response Bias

• Undercoverage

• Convenience Sampling

• Voluntary Response

Multiple Choice

Source of bias that occurs when you ask people who are EASY to ask

• Response Bias

• Convenience Sampling

• Nonresponse

• Voluntary Response

Multiple Choice

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

Multiple Choice

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