AP Statistics Unit 3: Gathering Data Practice Test and Study Guide

Comprehensive practice flashcards covering Unit 3: Gathering Data in AP Statistics, including sampling methods, bias, study types, experimental design, and statistical inference tools.

What data collection method gathers information from a portion of a population by asking questions?

Sample survey

What is the definition of a census?

A method that collects data from every member of a population.

What is the definition of an observational study?

A study where researchers observe subjects and measure variables without deliberately imposing or assigning treatments.

What is the definition of an experiment?

A study where researchers deliberately assign treatments to experimental units to investigate and study their effects.

What is a simulation in statistics?

A method that uses a model to imitate a real-world process.

Why is a sample survey the best method for an Internet search engine company to collect data on ease of use?

It collects users' opinions and preferences from a portion of the population, which is far more practical than attempting a census of all potential users.

In the Gallup Youth Survey of $1{,}028$ teens aged $13$ to $17$, what was the population of interest?

All U.S. teens aged $13$ to $17$.

In the Gallup Youth Survey about favorite movies from $2004$, what constituted the sample?

The $1{,}028$ teens who were actually surveyed.

In the Gallup Youth Survey, Napoleon Dynamite received $8\%$ of the votes. Why is this $8\%$ classified as a statistic rather than a parameter?

Because it is a numerical value calculated directly from the sample, rather than the true unknown value for the entire population.

What is the fundamental difference between a statistic and a parameter?

A statistic describes a characteristic of a sample, whereas a parameter describes a characteristic of an entire population.

Why can a randomly selected sample of $1{,}028$ teens provide a reasonably accurate estimate of the population percentage?

Random selection helps produce a representative sample and reduces selection bias, assuming nonresponse or other biases are not substantial.

What is the definition of a simple random sample (SRS)?

A sample selected in such a way that every possible group of a specified size has an equal chance of being selected.

A school board pools all students from three high schools and randomly samples $250$ students. Why is this an SRS even if some schools or grades are omitted?

Because every possible group of $250$ students across the entire district had an equal chance of selection; an SRS does not guarantee representation from every subgroup.

What is a stratified random sample?

A sampling design in which the population is divided into distinct groups called strata, and random samples are selected from each group.

What is undercoverage bias in sampling?

A bias that occurs when some groups of the population have a lower chance of being included in a sample or are systematically left out.

What is nonresponse bias?

A bias that occurs when selected individuals do not respond to a survey, potentially biasing results if their opinions differ from respondents.

What is response bias?

A bias that occurs when survey responses are systematically inaccurate because of the question wording, interviewer influence, or respondent behavior.

Why was the editor's concern about undercoverage justified when surveying students about campus security guards?

Chronically truant students are difficult to reach and may hold disproportionately negative views of security guards, distorting survey results if excluded.

What is the defining characteristic of a prospective study?

Data are collected as subjects or events are followed forward in time.

What is the defining characteristic of a retrospective study?

Researchers examine past events or existing records looking backward in time.

A researcher identifies $50$ healthy puppies and records their diets for several years to see if any develop thyroid problems. Why is this a prospective study?

Because the researcher starts with healthy subjects and follows them forward into the future to observe outcomes without imposing treatments.

Why does surveying only students who attend a large lecture class suffer from undercoverage when seeking to increase overall attendance?

Students who rarely or never attend are an important group for improving attendance, but they have little or no chance of being included in the survey.

What is voluntary response bias?

A bias that occurs when people choose whether to participate in an open invitation survey, often attracting individuals with strong opinions.

What is a placebo in an experiment?

A treatment designed to resemble the actual treatment without containing its active ingredient.

In experimental design, what is the primary purpose of using a placebo?

It is a tool for blinding that controls for the psychological effects of participant expectations.

What defines a single-blind experimental design?

One relevant group, commonly the participants, does not know the treatment assignment.

What defines a double-blind experimental design?

Both the participants and the evaluators who measure outcomes are unaware of treatment assignments.

Why is the statement 'no one knows which treatment any participant is receiving' incorrect regarding double-blind experiments?

Certain authorized researchers or medical personnel must have access to treatment assignments for safety, administration, or practical reasons.

What are the three fundamental principles of experimental design?

Control, randomization, and replication.

Which experimental design technique is optional rather than strictly required: control, randomization, replication, or blocking?

Blocking.

What is the definition of control in an experiment?

Keeping other conditions comparable between groups so that differences in outcomes can be attributed to the treatments.

What is the definition of replication in experimental design?

Applying each treatment to enough experimental units to assess variability and distinguish real treatment effects.

In the experiment comparing new and old shampoos across gender and dyed-hair groups, what was the treatment factor and its levels?

The treatment factor was shampoo type, with two levels: new shampoo and old shampoo.

In the shampoo experiment, what were the blocking variables?

Gender and whether hair is dyed.

What is a block in experimental design?

A group of similar experimental units formed before assigning treatments.

How was randomization carried out in the randomized block design of the shampoo experiment?

Subjects were randomly assigned to the new or old shampoo within each of the four blocks.

Why was the headline 'Video game playing can lead to better spatial reasoning abilities' inappropriate for an observational study?

The study compared existing groups without random assignment, establishing only an association rather than a cause-and-effect relationship.

In statistics, what does statistical significance mean?

The observed result would be unlikely to occur by chance alone under the study's specified null hypothesis, at the chosen significance level.

What study design can establish cause-and-effect relationships when properly designed?

A randomized experiment.

In the study where college students were assigned to three spending courses, what were the experimental units?

The individual college students.

In the college students' spending study, what was the factor and how many levels were investigated?

The factor was the type of course, and it had three levels.

In the college students' spending study, what was the response variable?

The students' spending habits, as measured by the researchers.

What is the definition of a treatment in an experiment?

A specific experimental condition assigned to experimental units.

Why was the preschool lunch bag temperature study classified as an observational study rather than an experiment?

Researchers measured the existing temperatures of lunches without deliberately assigning or imposing treatments.

Why was the preschool lunch study considered prospective rather than retrospective?

Researchers measured temperatures forward in time during the ongoing preparation and storage process, rather than reviewing past records.

What statistical inference tool should researchers use to estimate the true proportion of insulated lunches that reach unsafe temperatures?

A confidence interval for one population proportion.

What formula calculates the sample proportion $\hat{p}$?

$\hat{p} = \frac{x}{n}$, where $x$ is the number of successes and $n$ is the total sample size.

What is the general formula for a one-proportion confidence interval?

$$\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

In statistical inference for a population proportion, what component of a confidence interval is represented by the formula shown in the image?

The margin of error for a one-proportion confidence interval.

Which statistical inference method is appropriate when the research goal is to test a claim about a population mean?

A one-sample $t$-test.

Which statistical inference method is appropriate when the research goal is to estimate a population mean?

A confidence interval for one mean.

Which statistical inference method is appropriate when the research goal is to test a claim about a population proportion?

A one-proportion hypothesis test.