AP Statistics Flashcards: Complete 5-Unit Course Review
Review all five revised AP Statistics units with 250 original cards on data, study design, probability, inference, and regression.
เกี่ยวกับเด็คนี้
Review the revised five-unit AP Statistics course with 250 independently written English flashcards. The deck follows the framework effective fall 2026: Exploring One-Variable Data and Collecting Data; Probability, Random Variables, and Probability Distributions; Inference for Categorical Data: Proportions; Inference for Quantitative Data: Means; and Regression Analysis.
What the cards ask you to retrieve
- concept or condition → meaning
- scenario → appropriate method
- representation → interpretation
- result → contextual conclusion
- formula → use
- common error → correction
The order follows Units 1–5, with prerequisite ideas introduced before later inference and regression applications. Every card has the root ap-statistics tag and exactly one unit tag.
What's deliberately left out
This is a compact active-recall review, not a complete course, an official curriculum, or a promise of a particular score. It does not include full free-response questions, timed multiple-choice simulation, calculator-button tutorials, AP Classroom content, copied official examples, or scoring-guideline imitation.
Scope was reviewed against the official AP Statistics course page and the Course and Exam Description effective fall 2026. Check those official sources for current policies, exam details, and later revisions.
Statistical facts and the official course outline are not claimed as original. The CC0 dedication applies to the deck's independently written card wording, organization, and original cover to the extent the contributor can dedicate those elements.
This independent, unofficial deck is not affiliated with, endorsed by, or sponsored by the College Board. AP® and Advanced Placement® are trademarks owned by the College Board. No exam questions, scoring guidelines, curriculum passages, official examples, tables, logos, or trade dress are copied.
การ์ดในเด็คนี้
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What makes a question a statistical investigative question?
คำตอบ
It anticipates variability in data and can be answered by collecting and analyzing data about a population or process.
การ์ด 2
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What is an observational unit?
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An individual item or person from which data are collected.
การ์ด 3
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A student's class year is recorded as freshman, sophomore, junior, or senior. What type of variable is this?
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Categorical. The values name groups rather than measure a numerical amount.
การ์ด 4
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How does a parameter differ from a statistic?
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A parameter describes a population; a statistic describes a sample.
การ์ด 5
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How is a category's relative frequency calculated?
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Divide the category count by the total number of observations.
การ์ด 6
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What should the height of a bar represent in a relative-frequency bar chart?
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The proportion or percentage of observations in that category.
การ์ด 7
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Number of text messages sent in a day: discrete or continuous?
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Discrete. It is a count with separated possible values.
การ์ด 8
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Which displays preserve individual quantitative data values?
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Dotplots and stem-and-leaf plots. A histogram groups values into intervals.
การ์ด 9
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What four features should a description of a quantitative distribution address?
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Shape, center, variability, and unusual features such as gaps or outliers.
การ์ด 10
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Which measure of center is usually better for a strongly right-skewed distribution?
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The median, because it is resistant to extreme high values.
การ์ด 11
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The values are 3, 5, 5, and 11. What is the mean?
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- The sum is 24, divided by 4 observations.
การ์ด 12
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The ordered values are 2, 4, 7, 9, 12, and 20. What is the median?
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8, the average of the two middle values 7 and 9.
การ์ด 13
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How is the interquartile range calculated?
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IQR = Q3 − Q1. It measures the spread of the middle 50% of the data.
การ์ด 14
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What does a small standard deviation say about a data set?
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Values typically lie close to the mean.
การ์ด 15
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Which common summaries are resistant to extreme values?
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The median and IQR are resistant; the mean and standard deviation are not.
การ์ด 16
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In a modified boxplot, where do the whiskers end?
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At the smallest and largest observed values within the 1.5 × IQR fences; values beyond the fences are plotted separately as potential outliers.
การ์ด 17
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What are the 1.5 × IQR outlier fences?
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Lower fence = Q1 − 1.5(IQR); upper fence = Q3 + 1.5(IQR). Values beyond them are flagged as potential outliers.
การ์ด 18
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How should two quantitative distributions be compared?
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Compare shape, center, variability, and unusual features in context, using the same measure or display basis.
การ์ด 19
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What does a z-score of −1.8 mean?
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The value is 1.8 standard deviations below the mean.
การ์ด 20
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Every observation is converted from meters to centimeters by multiplying by 100. What happens to the mean and standard deviation?
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Both are multiplied by 100.
การ์ด 21
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What should an investigative question identify so the conclusion has a clear scope?
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The variable or parameter of interest and the population to which the conclusion may apply.
การ์ด 22
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What is a census?
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A study that collects data from every member of the population.
การ์ด 23
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What makes a study an experiment?
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Researchers deliberately assign treatments to experimental units.
การ์ด 24
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How do prospective and retrospective observational studies differ?
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A prospective study follows units forward and gathers future data; a retrospective study uses data from the past.
การ์ด 25
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What is a confounding variable in an observational study?
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A variable associated with both the explanatory and response variables that offers an alternative explanation for their relationship.
การ์ด 26
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What study feature supports generalizing results to a population?
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Random selection from that population.
การ์ด 27
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What makes a study observational?
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Researchers observe variables without assigning treatments.
การ์ด 28
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What study feature supports a cause-and-effect conclusion?
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Random assignment of treatments in a well-designed experiment.
การ์ด 29
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What defines a simple random sample of size n?
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Every possible sample of size n has the same chance of selection.
การ์ด 30
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What changes when sampling is done with replacement?
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A selected unit returns to the population and can be selected again.
การ์ด 31
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Why can a convenience sample be biased?
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Easy-to-reach units may differ systematically from the target population.
การ์ด 32
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Why should an experiment compare at least two treatment groups?
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The comparison provides a baseline for judging whether responses differ by treatment.
การ์ด 33
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A school samples 20 students at random from each grade. Which sampling method is this?
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Stratified random sampling, with grade as the stratum.
การ์ด 34
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What is the purpose of random assignment?
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It tends to balance lurking variables across treatment groups, supporting causal inference.
การ์ด 35
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Why can a voluntary-response sample be biased?
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People with strong opinions are often more likely to participate.
การ์ด 36
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What does replication mean in an experiment?
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Assigning more than one experimental unit to each treatment so treatment differences can be separated from individual variability.
การ์ด 37
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A city randomly selects 8 apartment buildings and surveys every household in those buildings. Which method is this?
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Cluster random sampling.
การ์ด 38
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What does direct control do in an experiment?
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It holds potential extraneous sources of variation constant across experimental units.
การ์ด 39
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What is undercoverage?
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Some groups in the target population are left out of, or poorly represented in, the sampling frame.
การ์ด 40
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What is the role of a control group?
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It supplies a comparison condition for evaluating the treatment of interest.
การ์ด 41
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After a random start, a quality inspector checks every 40th item. Which sampling method is this?
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Systematic random sampling.
การ์ด 42
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Why might an experiment use a placebo?
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To separate a treatment's effect from responses caused by expecting treatment.
การ์ด 43
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What is nonresponse bias?
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Selected individuals who do not respond differ in a relevant way from those who do.
การ์ด 44
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What is single blinding designed to reduce?
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Bias caused when participants or evaluators know which treatment was received, depending on who is blinded.
การ์ด 45
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Why use a randomized block design?
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To group units that are similar on an important source of variation, then compare treatments within each block.
การ์ด 46
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What defines a matched-pairs design?
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Two treatments are compared using paired similar units or by giving both treatments to each unit in randomized order.
การ์ด 47
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A survey asks, “Don't you agree the new schedule is unfair?” What problem does this create?
คำตอบ
Response bias from leading wording.
การ์ด 48
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What usually makes an experiment double-blind?
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Neither the participants nor the people evaluating responses know treatment assignments while outcomes are measured.
การ์ด 49
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A researcher randomly assigns 80 volunteers to two diets and compares blood-pressure change. What conclusion can random assignment support?
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A cause-and-effect conclusion for people similar to the volunteers, assuming the experiment is well designed; volunteer recruitment does not support broad population generalization.
การ์ด 50
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A researcher records coffee intake and sleep duration without assigning either. Can the study establish that coffee causes less sleep?
คำตอบ
No. It is observational, so confounding can provide alternative explanations.
การ์ด 51
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What is the difference between a population and a sample?
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The population is the full group of interest; a sample is the subset actually observed.
การ์ด 52
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Which graph is appropriate for the distribution of one quantitative variable measured on 600 people?
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A histogram is appropriate; it groups the many numerical values into intervals.
การ์ด 53
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In a strongly right-skewed distribution, how do the mean and median usually compare?
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The mean is usually larger because high values pull it to the right.
การ์ด 54
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Every score increases by 7 points. What happens to the mean and standard deviation?
คำตอบ
The mean increases by 7; the standard deviation stays unchanged.
การ์ด 55
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What does it mean that a score is at the 80th percentile?
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About 80% of scores are at or below it.
การ์ด 56
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Why should gaps and clusters be mentioned when describing a distribution?
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They may reveal distinct subgroups, collection effects, or other structure that center and spread alone hide.
การ์ด 57
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What is the minimum ethical safeguard when collecting identifiable human data?
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Obtain informed consent when required and protect participants' privacy and confidentiality.
การ์ด 58
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Every measurement is multiplied by −2. What happens to the mean and standard deviation?
คำตอบ
The mean is multiplied by −2; the standard deviation is multiplied by 2.
การ์ด 59
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A study uses random sampling but no assigned treatment. What can it support?
คำตอบ
Population generalization, but not a cause-and-effect conclusion.
การ์ด 60
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A report calls any unmeasured variable a confounder. What is the correction?
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A confounder must be related to both the explanatory and response variables and create an alternative explanation.
การ์ด 61
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What does a two-way table summarize?
คำตอบ
Counts or relative frequencies for combinations of two categorical variables.
การ์ด 62
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What is a joint relative frequency?
คำตอบ
A cell count divided by the grand total, representing one combination of categories.
การ์ด 63
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What is a marginal relative frequency?
คำตอบ
A row or column total divided by the grand total.
การ์ด 64
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How is a conditional relative frequency calculated within one row?
คำตอบ
Divide each cell in that row by the row total.
การ์ด 65
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What pattern suggests association between two categorical variables?
คำตอบ
The conditional distribution of one variable changes across categories of the other.
การ์ด 66
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Why are segmented bar charts useful for two categorical variables?
คำตอบ
They place conditional distributions on the same 100% scale, making category patterns easy to compare.
การ์ด 67
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How do an outcome and an event differ?
คำตอบ
An outcome is one result of a trial; an event is a set of one or more outcomes.
การ์ด 68
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What must a valid probability simulation specify?
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A chance mechanism whose outcomes match the event probabilities, one trial definition, the statistic recorded, and many repetitions.
การ์ด 69
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What does the law of large numbers predict?
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As independent trials accumulate, an event's long-run relative frequency tends to approach its probability.
การ์ด 70
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What two requirements must probabilities in a sample space satisfy?
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Each probability is between 0 and 1, and the probabilities of all nonoverlapping outcomes sum to 1.
การ์ด 71
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What is the complement rule?
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P(Aᶜ) = 1 − P(A). It is often useful for “at least one” events.
การ์ด 72
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How can you verify that events A and B are mutually exclusive?
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Their intersection is impossible, so P(A ∩ B) = 0.
การ์ด 73
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What is the formula for P(A | B), when P(B) > 0?
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P(A | B) = P(A ∩ B) / P(B). The restricted sample space is B.
การ์ด 74
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What is the general multiplication rule for two events?
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P(A ∩ B) = P(A)P(B | A), or equivalently P(B)P(A | B).
การ์ด 75
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What does it mean for events A and B to be independent?
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Knowing that one occurred does not change the probability of the other.
การ์ด 76
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What is the general addition rule?
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P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
การ์ด 77
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Why are two mutually exclusive events with positive probabilities not independent?
คำตอบ
If one occurs, the other cannot occur, so its conditional probability drops to 0.
การ์ด 78
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What is a random variable?
คำตอบ
A numerical value determined by the outcome of a random process.
การ์ด 79
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What makes a table a valid discrete probability distribution?
คำตอบ
It lists every possible value with probabilities from 0 to 1 that sum to 1.
การ์ด 80
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What does a cumulative distribution value F(x) represent?
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P(X ≤ x), the probability that the random variable is at most x.
การ์ด 81
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How is the expected value of a discrete random variable calculated?
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Multiply each possible value by its probability and add: E(X) = ΣxP(X = x).
การ์ด 82
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What does the standard deviation of a random variable measure?
คำตอบ
The typical distance of long-run outcomes from the random variable's mean.
การ์ด 83
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How is the standard deviation of a discrete random variable calculated?
คำตอบ
σₓ = √[Σ(x − μₓ)²P(X = x)]. The quantity inside the square root is Var(X).
การ์ด 84
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A game has E(X) = −$0.40 per play. What does this mean?
คำตอบ
Over many plays, the player's average net result approaches a loss of 40 cents per play; it does not predict every play.
การ์ด 85
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What conditions define a binomial random variable?
คำตอบ
A fixed number of independent trials, two outcomes per trial, constant success probability, and X counts successes.
การ์ด 86
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For X ~ Binomial(n, p), what are the mean and standard deviation?
คำตอบ
Mean = np; standard deviation = √[np(1 − p)].
การ์ด 87
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For X ~ Binomial(n, p), what is P(X = x)?
คำตอบ
Choose x success positions, then multiply: C(n, x)pˣ(1 − p)ⁿ⁻ˣ.
การ์ด 88
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How can P(X ≥ 1) be found efficiently for a binomial variable?
คำตอบ
Use the complement: P(X ≥ 1) = 1 − P(X = 0).
การ์ด 89
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What should one simulated trial represent when estimating P(X ≥ 4) for X ~ Binomial(10, 0.3)?
คำตอบ
Ten independent success/failure observations with success probability 0.3, followed by recording whether at least four successes occurred.
การ์ด 90
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What features characterize a normal distribution?
คำตอบ
It is continuous, symmetric, unimodal, and bell-shaped.
การ์ด 91
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Which parameters determine a normal distribution?
คำตอบ
Its mean μ sets the center, and its standard deviation σ sets the spread.
การ์ด 92
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What is the standard normal distribution?
คำตอบ
The normal distribution with mean 0 and standard deviation 1.
การ์ด 93
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What is the 68–95–99.7 rule?
คำตอบ
For an approximately normal distribution, about 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations of the mean.
การ์ด 94
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What does an area under a normal curve represent?
คำตอบ
The probability or population proportion within the corresponding interval.
การ์ด 95
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How do you find the value cutting off the lowest 10% of a normal distribution?
คำตอบ
Find the z-score with cumulative area 0.10, then convert with x = μ + zσ.
การ์ด 96
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A normal variable has μ = 50 and σ = 8. What z-score corresponds to x = 62?
คำตอบ
1.5, because z = (62 − 50) / 8.
การ์ด 97
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Two exam scores come from different normal distributions. What makes their percentiles comparable?
คำตอบ
Standardize each score with its own distribution's mean and standard deviation, then compare z-scores or cumulative areas.
การ์ด 98
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What is a sampling distribution of a statistic?
คำตอบ
The distribution of that statistic over all possible random samples of a fixed size from a population.
การ์ด 99
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How can a sampling distribution be approximated by simulation?
คำตอบ
Repeatedly take random samples of the same size, calculate the statistic each time, and graph the resulting values.
การ์ด 100
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What is a randomization distribution?
คำตอบ
A simulated distribution of a statistic produced by repeatedly reallocating responses or labels as specified by a null model.
การ์ด 101
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What does the central limit theorem say about sample means?
คำตอบ
For random samples, the sampling distribution of the sample mean becomes approximately normal as sample size grows, even when the population is not normal.
การ์ด 102
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How does increasing sample size affect the normal approximation in the central limit theorem?
คำตอบ
It generally improves the approximation, especially for skewed or irregular populations.
การ์ด 103
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A segmented bar chart shows nearly identical category proportions for every group. What does that suggest?
คำตอบ
Little or no association between the two categorical variables.
การ์ด 104
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In a survey, 30 of 120 students both bike to school and arrive before 8:00. What is the joint relative frequency?
คำตอบ
0.25, because 30 / 120 = 0.25.
การ์ด 105
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Why can P(A | B) differ from P(B | A)?
คำตอบ
They use different restricted sample spaces and usually have different denominators.
การ์ด 106
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If P(A) = 0.4 and P(A | B) = 0.4 with P(B) > 0, what does this indicate?
คำตอบ
A and B are independent because learning B does not change the probability of A.
การ์ด 107
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If independent events have probabilities 0.6 and 0.5, what is the probability that both occur?
คำตอบ
0.30, using P(A ∩ B) = P(A)P(B).
การ์ด 108
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A prize is $0 with probability 0.7 and $10 with probability 0.3. What is the expected prize?
คำตอบ
$3, because 0(0.7) + 10(0.3) = 3.
การ์ด 109
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A machine produces defective items independently with probability 0.02. What distribution models the number of defectives in 50 items?
คำตอบ
Binomial with n = 50 and p = 0.02.
การ์ด 110
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Heights are approximately normal with μ = 170 cm and σ = 6 cm. About what percent lie from 158 to 182 cm?
คำตอบ
About 95%, because the interval is μ ± 2σ.
การ์ด 111
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What makes an estimator unbiased?
คำตอบ
Its sampling distribution is centered at the population parameter it estimates.
การ์ด 112
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For random samples of size n, what is the mean of the sampling distribution of p̂?
คำตอบ
μₚ̂ = p, where p is the population proportion.
การ์ด 113
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Which procedure estimates one population proportion from a random sample?
คำตอบ
A one-sample z-interval for a population proportion.
การ์ด 114
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How should a confidence interval for a population proportion be interpreted?
คำตอบ
We are confident at the stated level that the interval captures the true population proportion, in context.
การ์ด 115
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What hypotheses test whether a population proportion differs from 0.40?
คำตอบ
H₀: p = 0.40 versus Hₐ: p ≠ 0.40.
การ์ด 116
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What is a p-value?
คำตอบ
Assuming H₀ is true, it is the probability of a test statistic as extreme as or more extreme than the observed statistic in the direction of Hₐ.
การ์ด 117
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What is the hypothesis-test decision rule using significance level α?
คำตอบ
Reject H₀ when the p-value ≤ α; otherwise fail to reject H₀.
การ์ด 118
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What is a Type I error?
คำตอบ
Rejecting H₀ when H₀ is actually true.
การ์ด 119
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What is the mean of p̂₁ − p̂₂ for independent random samples?
คำตอบ
p₁ − p₂.
การ์ด 120
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Which procedure estimates p₁ − p₂ from two independent samples or randomized groups?
คำตอบ
A two-sample z-interval for a difference between population proportions.
การ์ด 121
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How should a confidence interval for p₁ − p₂ be interpreted?
คำตอบ
We are confident at the stated level that the interval captures the true difference p₁ − p₂, in context.
การ์ด 122
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What null hypothesis is standard when testing whether two population proportions differ?
คำตอบ
H₀: p₁ − p₂ = 0, equivalently p₁ = p₂.
การ์ด 123
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A two-proportion test gives p-value 0.018 at α = 0.05. What decision follows?
คำตอบ
Reject H₀ because 0.018 < 0.05.
การ์ด 124
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When is a chi-square test for independence appropriate?
คำตอบ
When one random sample provides two categorical variables and the question asks whether they are associated in one population.
การ์ด 125
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How should a chi-square test p-value be interpreted?
คำตอบ
Assuming the null model of independence or homogeneity is true, it is the probability of a chi-square statistic at least as large as the one observed.
250 การ์ด
AP Statistics Flashcards: Complete 5-Unit Course Review
เรียนเด็คนี้ฟรีNibomo จะเปิดขึ้นเพื่อให้คุณเริ่มเรียนได้ทันที
การ์ด 126
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How do bias and variability differ for an estimator?
คำตอบ
Bias concerns where the sampling distribution is centered; variability concerns how spread out it is.
การ์ด 127
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What is the standard deviation of p̂ when observations are independent?
คำตอบ
σₚ̂ = √[p(1 − p) / n].
การ์ด 128
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What is the one-proportion z-interval formula?
คำตอบ
p̂ ± z*√[p̂(1 − p̂) / n].
การ์ด 129
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What does a 95% confidence level describe?
คำตอบ
In repeated random sampling with the same method, about 95% of the resulting intervals would capture the true parameter.
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คำถาม
Which method tests a claim about one population proportion when its conditions hold?
คำตอบ
A one-sample z-test for a population proportion.
การ์ด 131
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How does the alternative hypothesis determine a p-value's tail area?
คำตอบ
A greater-than alternative uses the upper tail, a less-than alternative uses the lower tail, and a not-equal alternative uses both tails.
การ์ด 132
คำถาม
What wording should follow a rejected null hypothesis?
คำตอบ
There is convincing statistical evidence for the alternative claim about the population parameter, stated in context.
การ์ด 133
คำถาม
What is a Type II error?
คำตอบ
Failing to reject H₀ when Hₐ is actually true.
การ์ด 134
คำถาม
What is the standard deviation of p̂₁ − p̂₂ for independent samples?
คำตอบ
√[p₁(1 − p₁)/n₁ + p₂(1 − p₂)/n₂].
การ์ด 135
คำถาม
What standard error is used in a confidence interval for p₁ − p₂?
คำตอบ
√[p̂₁(1 − p̂₁)/n₁ + p̂₂(1 − p̂₂)/n₂]; the sample proportions are not pooled.
การ์ด 136
คำถาม
A confidence interval for p₁ − p₂ contains 0. What does that imply?
คำตอบ
The interval does not provide convincing evidence of a difference between the population proportions at the corresponding two-sided significance level.
การ์ด 137
คำถาม
Why is a pooled proportion used in a two-proportion z-test with H₀: p₁ = p₂?
คำตอบ
The null model assumes both samples share one common population proportion, estimated by combining successes and observations.
การ์ด 138
คำถาม
How should a p-value for a two-proportion test be stated?
คำตอบ
Assuming the population proportions are equal, it is the probability of observing a difference in sample proportions at least as extreme as the one found, in the direction of Hₐ.
การ์ด 139
คำถาม
When is a chi-square test for homogeneity appropriate?
คำตอบ
When independent samples or randomized groups are compared on the distribution of one categorical response variable.
การ์ด 140
คำถาม
What is the chi-square test statistic formula?
คำตอบ
χ² = Σ[(observed − expected)² / expected], summed over all cells.
การ์ด 141
คำถาม
What usually happens to an estimator's sampling variability as sample size increases?
คำตอบ
It decreases; estimates from larger random samples tend to cluster more tightly around the parameter.
การ์ด 142
คำถาม
When is the sampling distribution of p̂ approximately normal?
คำตอบ
When the expected counts np and n(1 − p) are both at least 10.
การ์ด 143
คำถาม
What conditions justify a one-proportion z-interval?
คำตอบ
Random data; independence, checked with n ≤ 10% of the population when sampling without replacement; and at least 10 observed successes and 10 observed failures.
การ์ด 144
คำถาม
A 95% confidence interval for p is (0.52, 0.61). What does it say about the claim p = 0.50?
คำตอบ
The interval excludes 0.50, so the data provide evidence against p = 0.50 in a two-sided test at α = 0.05.
การ์ด 145
คำถาม
What is the one-proportion z-test statistic?
คำตอบ
z = (p̂ − p₀) / √[p₀(1 − p₀)/n], using the null proportion p₀ in the standard error.
การ์ด 146
คำถาม
How is a simulation-based p-value estimated?
คำตอบ
Find the proportion of simulated null statistics at least as extreme as the observed statistic in the direction of Hₐ.
การ์ด 147
คำถาม
What does “fail to reject H₀” mean?
คำตอบ
The data do not provide convincing evidence for Hₐ; it does not prove H₀ true.
การ์ด 148
คำถาม
With sample size and effect fixed, what often happens when α is lowered?
คำตอบ
The chance of a Type I error decreases, while the chance of a Type II error increases.
การ์ด 149
คำถาม
What conditions support the usual model for p̂₁ − p̂₂?
คำตอบ
Independent random samples or randomized groups, independence within each group, and large enough expected success and failure counts for normal approximation.
การ์ด 150
คำถาม
What conditions justify a two-proportion z-interval?
คำตอบ
Independent random samples or randomized groups; each sample no more than 10% of its population when sampling without replacement; and at least 10 observed successes and failures in each group.
การ์ด 151
คำถาม
How does increasing both sample sizes affect a confidence interval for p₁ − p₂?
คำตอบ
It reduces the standard error and usually narrows the interval when other factors stay the same.
การ์ด 152
คำถาม
What standard error is used in the two-proportion z-test?
คำตอบ
√[p̂c(1 − p̂c)(1/n₁ + 1/n₂)], where p̂c is the pooled sample proportion.
การ์ด 153
คำถาม
A randomized experiment uses volunteers assigned to two treatments. A significant two-proportion test supports what scope?
คำตอบ
A cause-and-effect conclusion for people similar to the volunteers, not automatic generalization to a broader population.
การ์ด 154
คำถาม
How is an expected count computed in a two-way table under independence?
คำตอบ
Expected count = (row total × column total) / grand total.
การ์ด 155
คำถาม
What conditions justify a chi-square test for a two-way table?
คำตอบ
Random data; independent observations, including the 10% check when sampling without replacement; and every expected cell count greater than 5.
การ์ด 156
คำถาม
A sampling distribution is centered away from the true parameter. What problem does this reveal?
คำตอบ
Bias in the estimator.
การ์ด 157
คำถาม
If p = 0.30 and n = 100, what does μₚ̂ = 0.30 mean?
คำตอบ
Across many random samples of 100, the average sample proportion would be 0.30.
การ์ด 158
คำถาม
For a planned proportion interval with margin of error m, what conservative p-value is used when no prior estimate exists?
คำตอบ
Use p* = 0.50 in n ≥ (z*/m)²p*(1 − p*) because it gives the largest required sample size.
การ์ด 159
คำถาม
What two changes widen a confidence interval for a proportion?
คำตอบ
Using a higher confidence level or a smaller sample size.
การ์ด 160
คำถาม
Which counts check normality for a one-proportion z-test?
คำตอบ
Use the null model: np₀ ≥ 10 and n(1 − p₀) ≥ 10.
การ์ด 161
คำถาม
What is wrong with saying “the p-value is the probability that H₀ is true”?
คำตอบ
The p-value assumes H₀ is true and measures how unusual the observed statistic would be under that assumption; it does not assign probability to H₀.
การ์ด 162
คำถาม
What does “statistically significant at α = 0.01” mean?
คำตอบ
The p-value is at most 0.01, so H₀ is rejected at that significance level.
การ์ด 163
คำถาม
What is the power of a hypothesis test?
คำตอบ
The probability that the test rejects H₀ when a particular alternative is true.
การ์ด 164
คำถาม
If p₁ = p₂, where is the sampling distribution of p̂₁ − p̂₂ centered?
คำตอบ
At 0, because its mean is p₁ − p₂.
การ์ด 165
คำถาม
Why must the order p̂₁ − p̂₂ stay consistent throughout an interval?
คำตอบ
Changing the order reverses the sign and changes the contextual interpretation of every endpoint.
การ์ด 166
คำถาม
A 95% interval for p₁ − p₂ is (0.04, 0.15). What conclusion is supported?
คำตอบ
p₁ is plausibly 0.04 to 0.15 higher than p₂; the interval supports a positive difference.
การ์ด 167
คำถาม
Which success-failure counts are checked for a two-proportion z-test?
คำตอบ
Expected counts based on the pooled null proportion: n₁p̂c, n₁(1 − p̂c), n₂p̂c, and n₂(1 − p̂c), each at least 10.
การ์ด 168
คำถาม
A two-proportion test with Hₐ: p₁ ≠ p₂ fails to reject H₀. What conclusion is valid?
คำตอบ
There is not convincing evidence that the two population proportions differ.
การ์ด 169
คำถาม
What are the degrees of freedom for a chi-square test on an r × c table?
คำตอบ
(r − 1)(c − 1).
การ์ด 170
คำถาม
A chi-square test for independence has a small p-value. What conclusion is appropriate?
คำตอบ
There is convincing evidence of an association between the two categorical variables in the population, stated in context.
การ์ด 171
คำถาม
What is the mean of the sampling distribution of x̄ for random samples from a population with mean μ?
คำตอบ
μₓ̄ = μ.
การ์ด 172
คำถาม
Which procedure estimates one population mean when the population standard deviation is unknown?
คำตอบ
A one-sample t-interval for a population mean.
การ์ด 173
คำถาม
How should a confidence interval for a population mean be interpreted?
คำตอบ
We are confident at the stated level that the interval captures the true population mean, in context.
การ์ด 174
คำถาม
What hypotheses test whether a population mean exceeds 12?
คำตอบ
H₀: μ = 12 versus Hₐ: μ > 12.
การ์ด 175
คำถาม
A one-sample t-test gives p-value 0.08 at α = 0.05. What decision follows?
คำตอบ
Fail to reject H₀ because 0.08 > 0.05.
การ์ด 176
คำถาม
What is the mean of x̄₁ − x̄₂ for independent random samples?
คำตอบ
μ₁ − μ₂.
การ์ด 177
คำถาม
Which procedure estimates μ₁ − μ₂ from two independent samples?
คำตอบ
A two-sample t-interval for a difference between population means.
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คำถาม
How should a confidence interval for μ₁ − μ₂ be interpreted?
คำตอบ
We are confident at the stated level that the interval captures the true difference μ₁ − μ₂, in context.
การ์ด 179
คำถาม
What null hypothesis is standard when testing whether two population means differ?
คำตอบ
H₀: μ₁ − μ₂ = 0, equivalently μ₁ = μ₂.
การ์ด 180
คำถาม
A two-sample t-test gives p-value 0.004 at α = 0.01. What decision follows?
คำตอบ
Reject H₀ because 0.004 < 0.01.
การ์ด 181
คำถาม
What is the standard deviation of x̄ when observations are independent?
คำตอบ
σₓ̄ = σ / √n.
การ์ด 182
คำถาม
What is the one-sample t-interval formula for μ?
คำตอบ
x̄ ± t* × s/√n, with t* based on n − 1 degrees of freedom.
การ์ด 183
คำถาม
What does a 90% confidence level mean for a mean interval procedure?
คำตอบ
Across many random samples using the same procedure, about 90% of the intervals would capture the true population mean.
การ์ด 184
คำถาม
Which procedure tests a claim about one population mean when σ is unknown?
คำตอบ
A one-sample t-test for a population mean.
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คำถาม
How should a one-mean test p-value be interpreted?
คำตอบ
Assuming the null mean is true, it is the probability of a t-statistic as extreme as or more extreme than observed in the direction of Hₐ.
การ์ด 186
คำถาม
What is the standard deviation of x̄₁ − x̄₂ for independent samples?
คำตอบ
√(σ₁²/n₁ + σ₂²/n₂).
การ์ด 187
คำถาม
What standard error is used in a two-sample t-interval for μ₁ − μ₂?
คำตอบ
√(s₁²/n₁ + s₂²/n₂).
การ์ด 188
คำถาม
A confidence interval for μ₁ − μ₂ contains 0. What does that imply?
คำตอบ
The interval does not provide convincing evidence of a difference between the population means at the corresponding two-sided significance level.
การ์ด 189
คำถาม
What is the two-sample t-statistic for testing H₀: μ₁ − μ₂ = 0?
คำตอบ
t = [(x̄₁ − x̄₂) − 0] / √(s₁²/n₁ + s₂²/n₂).
การ์ด 190
คำถาม
How should a two-mean test p-value be interpreted?
คำตอบ
Assuming the population means are equal, it is the probability of a sample-mean difference at least as extreme as observed, standardized in the direction of Hₐ.
การ์ด 191
คำถาม
When is the sampling distribution of x̄ approximately normal?
คำตอบ
When the population is approximately normal or the random sample is large enough for the central limit theorem to apply.
การ์ด 192
คำถาม
What conditions justify a one-sample t-interval?
คำตอบ
Random data; independence, checked with n ≤ 10% of the population when sampling without replacement; and for the Normal/Large Sample condition, n ≥ 30 is sufficient, while n < 30 requires sample data with no strong skewness or outliers.
การ์ด 193
คำถาม
How does increasing sample size affect a confidence interval for μ?
คำตอบ
It lowers the standard error and usually narrows the interval when confidence level and variability stay comparable.
การ์ด 194
คำถาม
What is the one-sample t-test statistic?
คำตอบ
t = (x̄ − μ₀) / (s/√n), with n − 1 degrees of freedom.
การ์ด 195
คำถาม
A t-test fails to reject H₀. What should the conclusion avoid?
คำตอบ
Avoid saying H₀ is true; say the data do not provide convincing evidence for Hₐ.
การ์ด 196
คำถาม
When is x̄₁ − x̄₂ approximately normal?
คำตอบ
When both populations are approximately normal or both independent random samples are large enough for normal approximations.
การ์ด 197
คำถาม
What conditions justify a two-sample t-interval?
คำตอบ
Independent random samples or randomized groups; each sample no more than 10% of its population when sampling without replacement; and for the Normal/Large Sample condition, both sample sizes ≥ 30 are sufficient, while either sample below 30 requires sample data with no strong skewness or outliers.
การ์ด 198
คำถาม
A 95% interval for μ₁ − μ₂ is (−7.2, −1.4). What does it support?
คำตอบ
μ₁ is plausibly 1.4 to 7.2 units lower than μ₂; the interval supports a negative difference.
การ์ด 199
คำถาม
What sample-shape condition is checked for a two-sample t-test with small samples?
คำตอบ
Both sample distributions should be free of strong skewness and outliers unless both populations are known to be approximately normal.
การ์ด 200
คำถาม
A randomized experiment finds a significant difference in mean response. What can random assignment support?
คำตอบ
A cause-and-effect conclusion for units like those studied, assuming the experiment was well designed.
การ์ด 201
คำถาม
A population has μ = 40. What does μₓ̄ = 40 mean for samples of size 25?
คำตอบ
Across all random samples of 25, the average sample mean is 40.
การ์ด 202
คำถาม
How is a matched-pairs confidence interval analyzed?
คำตอบ
Compute one difference for each pair, then use a one-sample t-interval on the population mean difference.
การ์ด 203
คำถาม
A 95% confidence interval for μ is (18.2, 21.7). What does it say about μ = 22?
คำตอบ
The interval excludes 22, providing evidence against μ = 22 in a two-sided test at α = 0.05.
การ์ด 204
คำถาม
Which observations enter a matched-pairs t-test?
คำตอบ
The within-pair differences, not the two original columns treated as independent samples.
การ์ด 205
คำถาม
A test reports p-value 0.032. At which common levels is it significant: 0.05 or 0.01?
คำตอบ
Significant at 0.05, but not at 0.01.
การ์ด 206
คำถาม
If μ₁ − μ₂ = 5, where is the sampling distribution of x̄₁ − x̄₂ centered?
คำตอบ
At 5.
การ์ด 207
คำถาม
Does the standard AP two-sample t procedure require equal population variances?
คำตอบ
No. It uses separate sample variances in the standard error rather than pooling them.
การ์ด 208
คำถาม
What two changes usually widen a confidence interval for μ₁ − μ₂?
คำตอบ
Higher confidence or smaller sample sizes.
การ์ด 209
คำถาม
Why must the order x̄₁ − x̄₂ match the order μ₁ − μ₂ in the hypotheses?
คำตอบ
Reversing the order reverses the sign and changes the direction of the claim.
การ์ด 210
คำถาม
A two-sample test with Hₐ: μ₁ > μ₂ fails to reject H₀. What conclusion is valid?
คำตอบ
There is not convincing evidence that μ₁ exceeds μ₂.
การ์ด 211
คำถาม
A population has σ = 18 and random samples have n = 36. What is σₓ̄?
คำตอบ
3, because 18/√36 = 3.
การ์ด 212
คำถาม
Why is a t distribution used for inference about a mean when σ is unknown?
คำตอบ
Replacing σ with the sample standard deviation s adds uncertainty, which the heavier-tailed t distribution accounts for.
การ์ด 213
คำถาม
What conditions justify a one-sample t-test?
คำตอบ
Random data; independence, checked with n ≤ 10% of the population when sampling without replacement; and for the Normal/Large Sample condition, n ≥ 30 is sufficient, while n < 30 requires sample data with no strong skewness or outliers.
การ์ด 214
คำถาม
What distinguishes a two-sample means procedure from a matched-pairs procedure?
คำตอบ
Two-sample procedures use independent groups; matched-pairs procedures analyze linked observations through their differences.
การ์ด 215
คำถาม
How are degrees of freedom handled for a two-sample t procedure?
คำตอบ
Technology usually uses an approximation based on both sample variances and sizes; a conservative fallback uses the smaller of n₁ − 1 and n₂ − 1.
การ์ด 216
คำถาม
What type of variables belong on a scatterplot?
คำตอบ
Two quantitative variables measured on the same observational units.
การ์ด 217
คำถาม
What does the correlation coefficient r describe?
คำตอบ
The direction and strength of a linear relationship between two quantitative variables.
การ์ด 218
คำถาม
What does ŷ = a + bx represent?
คำตอบ
A linear regression model predicting response y from explanatory variable x.
การ์ด 219
คำถาม
What is a residual?
คำตอบ
Observed response minus predicted response: residual = y − ŷ.
การ์ด 220
คำถาม
What makes a regression line the least-squares line?
คำตอบ
It minimizes the sum of squared residuals.
การ์ด 221
คำถาม
What four features should a scatterplot description address?
คำตอบ
Direction, form, strength, and unusual features such as outliers or clusters.
การ์ด 222
คำถาม
What values can r take?
คำตอบ
Any value from −1 to 1, inclusive.
การ์ด 223
คำถาม
How is the slope b interpreted in context?
คำตอบ
For each one-unit increase in x, the predicted value of y changes by b units on average.
การ์ด 224
คำถาม
What does a positive residual mean?
คำตอบ
The observed response is above the model's predicted response.
การ์ด 225
คำถาม
What is the least-squares slope formula?
คำตอบ
b = r(sᵧ/sₓ).
การ์ด 226
คำถาม
A scatterplot trends downward from left to right. What direction is the association?
คำตอบ
Negative: larger x-values tend to occur with smaller y-values.
การ์ด 227
คำถาม
Why can r be near 0 even when two variables are strongly related?
คำตอบ
Correlation measures only linear association, so a strong curved relationship can have r near 0.
การ์ด 228
คำถาม
How is the intercept a interpreted in context?
คำตอบ
It is the predicted response when x = 0, provided x = 0 is meaningful and within the data's scope.
การ์ด 229
คำถาม
A model predicts 18, and the observed response is 21. What is the residual?
คำตอบ
3, because 21 − 18 = 3.
การ์ด 230
คำถาม
How is the least-squares intercept found from the slope?
คำตอบ
a = ȳ − bx̄.
การ์ด 231
คำถาม
What makes a linear association look strong?
คำตอบ
The points lie close to a straight-line pattern, regardless of whether the slope is steep or shallow.
การ์ด 232
คำถาม
Does r have measurement units?
คำตอบ
No. Correlation is unitless because it is based on standardized values.
การ์ด 233
คำถาม
For ŷ = 12 + 2.5x, what is predicted when x = 4?
คำตอบ
22, because 12 + 2.5(4) = 22.
การ์ด 234
คำถาม
What residual-plot pattern supports using a linear model?
คำตอบ
Random scatter around zero with no clear curve, trend, or changing spread.
การ์ด 235
คำถาม
What does r² measure in simple linear regression?
คำตอบ
The proportion of variation in the response variable explained by its linear relationship with the explanatory variable.
การ์ด 236
คำถาม
A scatterplot shows a strong association. Does that establish causation?
คำตอบ
No. A scatterplot alone cannot rule out confounding or other explanations.
การ์ด 237
คำถาม
Why should unusual points be checked before interpreting r?
คำตอบ
Correlation is not resistant; an outlier or influential point can change r substantially.
การ์ด 238
คำถาม
Why is extrapolation risky?
คำตอบ
The relationship observed over the data range may not continue beyond that range.
การ์ด 239
คำถาม
A point lies below the regression line. What sign is its residual?
คำตอบ
Negative, because observed y is less than predicted ŷ.
การ์ด 240
คำถาม
Which point always lies on a least-squares regression line with an intercept?
คำตอบ
The point (x̄, ȳ).
การ์ด 241
คำถาม
Which variable goes on each axis of a scatterplot used for prediction?
คำตอบ
The explanatory variable goes on the horizontal x-axis; the response variable goes on the vertical y-axis.
การ์ด 242
คำถาม
What happens to r if the roles of x and y are swapped?
คำตอบ
Nothing. Correlation is symmetric.
การ์ด 243
คำถาม
What is interpolation?
คำตอบ
Predicting a response for an x-value within the range of observed explanatory values.
การ์ด 244
คำถาม
A residual plot has a clear U-shape. What is the correction?
คำตอบ
Do not treat the linear model as adequate; the curved pattern shows systematic structure remains.
การ์ด 245
คำถาม
A regression has r² = 0.64. What does this mean?
คำตอบ
About 64% of the variation in the response is explained by its linear relationship with the explanatory variable.
การ์ด 246
คำถาม
What is an outlier in a scatterplot?
คำตอบ
A point that falls away from the overall pattern of the other points.
การ์ด 247
คำถาม
What happens to r when x is converted from centimeters to meters?
คำตอบ
It stays the same because multiplying by a positive constant does not change standardized linear association.
การ์ด 248
คำถาม
When can a regression relationship support a causal conclusion?
คำตอบ
Only when the data come from a well-designed randomized experiment and the conclusion matches its scope.
การ์ด 249
คำถาม
What units does a residual use?
คำตอบ
The same units as the response variable y.
การ์ด 250
คำถาม
What is an influential point in regression?
คำตอบ
A point whose removal substantially changes the fitted regression line or another key regression result.
250 การ์ด
AP Statistics Flashcards: Complete 5-Unit Course Review
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