Unit Test: Collecting Data (AP STATS KHAN)

Annabella was curious about why people choose to skydive. She randomly selected 101010 flights that were carrying skydivers and interviewed all of the skydivers on the flights about their motivations.

A simple survey

Mia is considering moving to a different apartment complex than where she currently lives. To better understand rent prices, she takes a large random sample of apartment complexes in her city and finds out the monthly cost of rent for a 111-bedroom apartment at those complexes. She finds the average rent of apartments in the sample is about \$800$800dollar sign, 800 per month.

All 1-bedroom apartments in her city only

A recent study showed that viral medications might be useful for fighting certain bacterial infections. Participants with gastrointestinal issues were assigned to either a placebo or viral medication for the first four weeks of the study, followed by an additional four weeks on the other treatment. Their symptoms showed significantly more improvement from the viral medication than the placebo.

An experiment where the type of treatment (viral or placebo) is the explanatory variable

Researchers working on a vaccine for HIV recruited over 16{,}00016,00016, comma, 000 volunteers for an experiment. Each volunteer was randomly assigned to receive monthly injections of either the vaccine or a placebo for a year. The researchers were curious if subjects who received the vaccine would be less likely to contract HIV than subjects who received the placebo.

Both the subjects and the researchers are unaware of who is receiving the vaccine and who is receiving the placebo.

A quality control worker at a factory selects the first 101010 items she sees as her sample for the day.

Convenience sample

A news program invites its viewers to call in and share their position on a proposed tax increase. Ninety percent of the viewers that call in say that they will vote against the tax increase. For which population is 90\%90%90, percent a legitimate estimate of the percent of voters who will vote against the tax increase?

Only those viewers who called in

An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They select a random sample of 200020002000 customers who have made purchases in the past year. Half of the males are randomly assigned to the treatment group, and the other half are assigned to the control group. The same method is used to randomly assign half of the females to the treatment group and the other half to the control group.

Randomized block

A college professor wants to survey a sample of students taking his course. Here are some details about his course: He teaches 555 sections of the course. There are 250250250 total students across those sections. There are 505050 graduate students and 200200200 undergraduate students taking the course. Each section has about 505050 students (some graduate and some undergraduate). The professor wants to take a sample of 303030 students for a survey. He suspects that opinions on the survey may differ the most based on student type (graduate or undergraduate), so he wants to design his sample to take that into account.

Randomly select 666 graduate students and 242424 undergraduate students for the survey.

A college professor wants to survey a sample of students taking her large lecture course. There are about 150150150 students in the course, and 101010 of those students are graduate students. She wants to take a systematic random sample of approximately 303030 students.

Randomly select one of the first 555 students to arrive to class, and every 5^\text{th}5th5, start superscript, start text, t, h, end text, end superscript student thereafter to take the survey.

An airline wants to survey customers about their overall satisfaction. They take a random sample of 1{,}0001,0001, comma, 000 customers who have flown in the past month and email them a survey. The email also offers those who complete the survey a \$25$25dollar sign, 25 gift card that can be used almost anywhere.

Satisfied customers might be less likely to complete the survey than dissatisfied customers.

Security workers at an airport randomly choose one of the first 505050 people to pass through a checkpoint for extra security screening. After that person, they choose every 50^\text{th}50th50, start superscript, start text, t, h, end text, end superscript person who passes through for extra screening as well.

Systematic Random Sample

An education researcher wonders if young students better learn arithmetic facts using physical flashcards or a new online game. The researcher recruits 505050 students for a study. The study allows parents to choose which learning tool they'd like their child to use: flashcards or the online game. Each student takes a pre-test and a post-test, and at the end of the study, students who used flashcards show significantly better outcomes than students who used the online game. The researcher concludes that flashcards were more effective than the online game for this group of students.

The parents' choice of which learning tool their child uses

The state Department of Transportation wants to know about out-of-state vehicles that pass over a toll bridge with several lanes. A camera installed over one lane of the bridge photographs the license plate of every tenth vehicle that passes through that lane.

The population is all of the vehicles that pass through the lane with the camera; the sample is the group of every tenth vehicle that passes through the lane.

The owners of a sports stadium wanted to predict what additional refreshment options would sell well. They selected 808080 seat numbers at random and surveyed the occupants of those seats.

The population is the occupants of all seats in the sports stadium; the sample is the occupants of the 808080 selected seats.

A class was curious if their teacher could grade and return double-spaced papers faster than single-spaced papers. For a certain assignment, each student flipped a coin to determine if they would single-space or double-space their paper. The students agreed to all use the same font. The students who double-spaced received their graded papers back significantly faster than students who single-spaced. The class concluded that any teacher can grade and return papers faster if they are double-spaced rather than single-spaced.

The study was an experiment, but it didn't include anyone other than their teacher.

A recent study showed that players of a certain video game tend to perform better if they take breaks. The study involved analyzing data from 242{,}000242,000242, comma, 000 matches played by 16{,}66516,66516, comma, 665 players of League of Legends, a popular online game. The data showed that players who took regular breaks, on average, performed better than those who did not.

There was an association between taking breaks and better performance, but it's not necessarily a causal relationship.

A team of psychologists was curious if omega-3 fatty acid supplements could help treat depression in adolescents. They recruited 505050 adolescents with varying levels of depression to participate in an experiment. The researchers randomly assigned each subject to take either an omega-3 supplement or a placebo daily, and they monitored subjects' depression levels throughout the study.

To create groups that are as similar as possible so the main difference between the groups is the treatment

Willy runs a small company with 101010 employees. He decides to pick a simple random sample of 333 employees to go on a business trip. He numbers them 000-999 and uses the random digit table printed below to select the sample. Which employees are in the sample? 67197\,\, 28310\,\, 90341671972831090341

6,7,1

An online retailer wants to study whether more lenient return policies increase purchasing behaviors. They select a random sample of 200020002000 customers who have made purchases in the past year. The company ranks the customers according to total cost of purchases made the previous year. For every 222 customers, in order, from the list, the online retailer randomly assigns one customer to the treatment group and the other to the control group.

Matched pairs

Roshanda was curious if students in her class would complete a maze faster if fast-paced music was playing in the background. She randomly assigned each student in her class to one of three groups: fast-paced music, slow-paced music, or no music. She timed each student as they individually completed a maze with their corresponding music (or no music) in the background. Students who worked with the fast-paced music, on average, completed the maze significantly faster than students in the other groups.

Yes, the students were randomly assigned to treatment and control groups.

There are 909090 students in a lunch period, and 555 of them will be selected at random for cleaning duty every week. Each student receives a number 010101-909090 and the school uses a random digit table to select a simple random sample of 555 students. Which 555 students should be assigned cleaning duty? 24709\,\, 73698\,\, 14526\,\, 31893\,\, 325922470973698145263189332592

24,70,36,14,52

A polling firm wants to contact a random sample of people likely to vote in an upcoming nation-wide election. They will use a random digit dialer to generate and call phone numbers at random, so the poll will include people with landlines, unlisted numbers, and mobile phones. The random digit dialer skips invalid phone numbers. If a person doesn't answer a call, the dialer will try one more time, and then skip that number. When a person does answer, a pollster asks a set of initial questions—such as the person's age and whether or not they voted in previous elections—to see if they are likely to vote in the upcoming election. If they are eligible and likely to vote, the pollster will then ask a series of questions about the election.The poll excludes people too young to vote.

The poll excludes people too young to vote.