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.
Về bộ thẻ này
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.
Thẻ trong bộ này
Thẻ 1
Câu hỏi
What makes a question a statistical investigative question?
Câu trả lời
It anticipates variability in data and can be answered by collecting and analyzing data about a population or process.
Thẻ 2
Câu hỏi
What is an observational unit?
Câu trả lời
An individual item or person from which data are collected.
Thẻ 3
Câu hỏi
A student's class year is recorded as freshman, sophomore, junior, or senior. What type of variable is this?
Câu trả lời
Categorical. The values name groups rather than measure a numerical amount.
Thẻ 4
Câu hỏi
How does a parameter differ from a statistic?
Câu trả lời
A parameter describes a population; a statistic describes a sample.
Thẻ 5
Câu hỏi
How is a category's relative frequency calculated?
Câu trả lời
Divide the category count by the total number of observations.
Thẻ 6
Câu hỏi
What should the height of a bar represent in a relative-frequency bar chart?
Câu trả lời
The proportion or percentage of observations in that category.
Thẻ 7
Câu hỏi
Number of text messages sent in a day: discrete or continuous?
Câu trả lời
Discrete. It is a count with separated possible values.
Thẻ 8
Câu hỏi
Which displays preserve individual quantitative data values?
Câu trả lời
Dotplots and stem-and-leaf plots. A histogram groups values into intervals.
Thẻ 9
Câu hỏi
What four features should a description of a quantitative distribution address?
Câu trả lời
Shape, center, variability, and unusual features such as gaps or outliers.
Thẻ 10
Câu hỏi
Which measure of center is usually better for a strongly right-skewed distribution?
Câu trả lời
The median, because it is resistant to extreme high values.
Thẻ 11
Câu hỏi
The values are 3, 5, 5, and 11. What is the mean?
Câu trả lời
- The sum is 24, divided by 4 observations.
Thẻ 12
Câu hỏi
The ordered values are 2, 4, 7, 9, 12, and 20. What is the median?
Câu trả lời
8, the average of the two middle values 7 and 9.
Thẻ 13
Câu hỏi
How is the interquartile range calculated?
Câu trả lời
IQR = Q3 − Q1. It measures the spread of the middle 50% of the data.
Thẻ 14
Câu hỏi
What does a small standard deviation say about a data set?
Câu trả lời
Values typically lie close to the mean.
Thẻ 15
Câu hỏi
Which common summaries are resistant to extreme values?
Câu trả lời
The median and IQR are resistant; the mean and standard deviation are not.
Thẻ 16
Câu hỏi
In a modified boxplot, where do the whiskers end?
Câu trả lời
At the smallest and largest observed values within the 1.5 × IQR fences; values beyond the fences are plotted separately as potential outliers.
Thẻ 17
Câu hỏi
What are the 1.5 × IQR outlier fences?
Câu trả lời
Lower fence = Q1 − 1.5(IQR); upper fence = Q3 + 1.5(IQR). Values beyond them are flagged as potential outliers.
Thẻ 18
Câu hỏi
How should two quantitative distributions be compared?
Câu trả lời
Compare shape, center, variability, and unusual features in context, using the same measure or display basis.
Thẻ 19
Câu hỏi
What does a z-score of −1.8 mean?
Câu trả lời
The value is 1.8 standard deviations below the mean.
Thẻ 20
Câu hỏi
Every observation is converted from meters to centimeters by multiplying by 100. What happens to the mean and standard deviation?
Câu trả lời
Both are multiplied by 100.
Thẻ 21
Câu hỏi
What should an investigative question identify so the conclusion has a clear scope?
Câu trả lời
The variable or parameter of interest and the population to which the conclusion may apply.
Thẻ 22
Câu hỏi
What is a census?
Câu trả lời
A study that collects data from every member of the population.
Thẻ 23
Câu hỏi
What makes a study an experiment?
Câu trả lời
Researchers deliberately assign treatments to experimental units.
Thẻ 24
Câu hỏi
How do prospective and retrospective observational studies differ?
Câu trả lời
A prospective study follows units forward and gathers future data; a retrospective study uses data from the past.
Thẻ 25
Câu hỏi
What is a confounding variable in an observational study?
Câu trả lời
A variable associated with both the explanatory and response variables that offers an alternative explanation for their relationship.
Thẻ 26
Câu hỏi
What study feature supports generalizing results to a population?
Câu trả lời
Random selection from that population.
Thẻ 27
Câu hỏi
What makes a study observational?
Câu trả lời
Researchers observe variables without assigning treatments.
Thẻ 28
Câu hỏi
What study feature supports a cause-and-effect conclusion?
Câu trả lời
Random assignment of treatments in a well-designed experiment.
Thẻ 29
Câu hỏi
What defines a simple random sample of size n?
Câu trả lời
Every possible sample of size n has the same chance of selection.
Thẻ 30
Câu hỏi
What changes when sampling is done with replacement?
Câu trả lời
A selected unit returns to the population and can be selected again.
Thẻ 31
Câu hỏi
Why can a convenience sample be biased?
Câu trả lời
Easy-to-reach units may differ systematically from the target population.
Thẻ 32
Câu hỏi
Why should an experiment compare at least two treatment groups?
Câu trả lời
The comparison provides a baseline for judging whether responses differ by treatment.
Thẻ 33
Câu hỏi
A school samples 20 students at random from each grade. Which sampling method is this?
Câu trả lời
Stratified random sampling, with grade as the stratum.
Thẻ 34
Câu hỏi
What is the purpose of random assignment?
Câu trả lời
It tends to balance lurking variables across treatment groups, supporting causal inference.
Thẻ 35
Câu hỏi
Why can a voluntary-response sample be biased?
Câu trả lời
People with strong opinions are often more likely to participate.
Thẻ 36
Câu hỏi
What does replication mean in an experiment?
Câu trả lời
Assigning more than one experimental unit to each treatment so treatment differences can be separated from individual variability.
Thẻ 37
Câu hỏi
A city randomly selects 8 apartment buildings and surveys every household in those buildings. Which method is this?
Câu trả lời
Cluster random sampling.
Thẻ 38
Câu hỏi
What does direct control do in an experiment?
Câu trả lời
It holds potential extraneous sources of variation constant across experimental units.
Thẻ 39
Câu hỏi
What is undercoverage?
Câu trả lời
Some groups in the target population are left out of, or poorly represented in, the sampling frame.
Thẻ 40
Câu hỏi
What is the role of a control group?
Câu trả lời
It supplies a comparison condition for evaluating the treatment of interest.
Thẻ 41
Câu hỏi
After a random start, a quality inspector checks every 40th item. Which sampling method is this?
Câu trả lời
Systematic random sampling.
Thẻ 42
Câu hỏi
Why might an experiment use a placebo?
Câu trả lời
To separate a treatment's effect from responses caused by expecting treatment.
Thẻ 43
Câu hỏi
What is nonresponse bias?
Câu trả lời
Selected individuals who do not respond differ in a relevant way from those who do.
Thẻ 44
Câu hỏi
What is single blinding designed to reduce?
Câu trả lời
Bias caused when participants or evaluators know which treatment was received, depending on who is blinded.
Thẻ 45
Câu hỏi
Why use a randomized block design?
Câu trả lời
To group units that are similar on an important source of variation, then compare treatments within each block.
Thẻ 46
Câu hỏi
What defines a matched-pairs design?
Câu trả lời
Two treatments are compared using paired similar units or by giving both treatments to each unit in randomized order.
Thẻ 47
Câu hỏi
A survey asks, “Don't you agree the new schedule is unfair?” What problem does this create?
Câu trả lời
Response bias from leading wording.
Thẻ 48
Câu hỏi
What usually makes an experiment double-blind?
Câu trả lời
Neither the participants nor the people evaluating responses know treatment assignments while outcomes are measured.
Thẻ 49
Câu hỏi
A researcher randomly assigns 80 volunteers to two diets and compares blood-pressure change. What conclusion can random assignment support?
Câu trả lời
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.
Thẻ 50
Câu hỏi
A researcher records coffee intake and sleep duration without assigning either. Can the study establish that coffee causes less sleep?
Câu trả lời
No. It is observational, so confounding can provide alternative explanations.
Thẻ 51
Câu hỏi
What is the difference between a population and a sample?
Câu trả lời
The population is the full group of interest; a sample is the subset actually observed.
Thẻ 52
Câu hỏi
Which graph is appropriate for the distribution of one quantitative variable measured on 600 people?
Câu trả lời
A histogram is appropriate; it groups the many numerical values into intervals.
Thẻ 53
Câu hỏi
In a strongly right-skewed distribution, how do the mean and median usually compare?
Câu trả lời
The mean is usually larger because high values pull it to the right.
Thẻ 54
Câu hỏi
Every score increases by 7 points. What happens to the mean and standard deviation?
Câu trả lời
The mean increases by 7; the standard deviation stays unchanged.
Thẻ 55
Câu hỏi
What does it mean that a score is at the 80th percentile?
Câu trả lời
About 80% of scores are at or below it.
Thẻ 56
Câu hỏi
Why should gaps and clusters be mentioned when describing a distribution?
Câu trả lời
They may reveal distinct subgroups, collection effects, or other structure that center and spread alone hide.
Thẻ 57
Câu hỏi
What is the minimum ethical safeguard when collecting identifiable human data?
Câu trả lời
Obtain informed consent when required and protect participants' privacy and confidentiality.
Thẻ 58
Câu hỏi
Every measurement is multiplied by −2. What happens to the mean and standard deviation?
Câu trả lời
The mean is multiplied by −2; the standard deviation is multiplied by 2.
Thẻ 59
Câu hỏi
A study uses random sampling but no assigned treatment. What can it support?
Câu trả lời
Population generalization, but not a cause-and-effect conclusion.
Thẻ 60
Câu hỏi
A report calls any unmeasured variable a confounder. What is the correction?
Câu trả lời
A confounder must be related to both the explanatory and response variables and create an alternative explanation.
Thẻ 61
Câu hỏi
What does a two-way table summarize?
Câu trả lời
Counts or relative frequencies for combinations of two categorical variables.
Thẻ 62
Câu hỏi
What is a joint relative frequency?
Câu trả lời
A cell count divided by the grand total, representing one combination of categories.
Thẻ 63
Câu hỏi
What is a marginal relative frequency?
Câu trả lời
A row or column total divided by the grand total.
Thẻ 64
Câu hỏi
How is a conditional relative frequency calculated within one row?
Câu trả lời
Divide each cell in that row by the row total.
Thẻ 65
Câu hỏi
What pattern suggests association between two categorical variables?
Câu trả lời
The conditional distribution of one variable changes across categories of the other.
Thẻ 66
Câu hỏi
Why are segmented bar charts useful for two categorical variables?
Câu trả lời
They place conditional distributions on the same 100% scale, making category patterns easy to compare.
Thẻ 67
Câu hỏi
How do an outcome and an event differ?
Câu trả lời
An outcome is one result of a trial; an event is a set of one or more outcomes.
Thẻ 68
Câu hỏi
What must a valid probability simulation specify?
Câu trả lời
A chance mechanism whose outcomes match the event probabilities, one trial definition, the statistic recorded, and many repetitions.
Thẻ 69
Câu hỏi
What does the law of large numbers predict?
Câu trả lời
As independent trials accumulate, an event's long-run relative frequency tends to approach its probability.
Thẻ 70
Câu hỏi
What two requirements must probabilities in a sample space satisfy?
Câu trả lời
Each probability is between 0 and 1, and the probabilities of all nonoverlapping outcomes sum to 1.
Thẻ 71
Câu hỏi
What is the complement rule?
Câu trả lời
P(Aᶜ) = 1 − P(A). It is often useful for “at least one” events.
Thẻ 72
Câu hỏi
How can you verify that events A and B are mutually exclusive?
Câu trả lời
Their intersection is impossible, so P(A ∩ B) = 0.
Thẻ 73
Câu hỏi
What is the formula for P(A | B), when P(B) > 0?
Câu trả lời
P(A | B) = P(A ∩ B) / P(B). The restricted sample space is B.
Thẻ 74
Câu hỏi
What is the general multiplication rule for two events?
Câu trả lời
P(A ∩ B) = P(A)P(B | A), or equivalently P(B)P(A | B).
Thẻ 75
Câu hỏi
What does it mean for events A and B to be independent?
Câu trả lời
Knowing that one occurred does not change the probability of the other.
Thẻ 76
Câu hỏi
What is the general addition rule?
Câu trả lời
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Thẻ 77
Câu hỏi
Why are two mutually exclusive events with positive probabilities not independent?
Câu trả lời
If one occurs, the other cannot occur, so its conditional probability drops to 0.
Thẻ 78
Câu hỏi
What is a random variable?
Câu trả lời
A numerical value determined by the outcome of a random process.
Thẻ 79
Câu hỏi
What makes a table a valid discrete probability distribution?
Câu trả lời
It lists every possible value with probabilities from 0 to 1 that sum to 1.
Thẻ 80
Câu hỏi
What does a cumulative distribution value F(x) represent?
Câu trả lời
P(X ≤ x), the probability that the random variable is at most x.
Thẻ 81
Câu hỏi
How is the expected value of a discrete random variable calculated?
Câu trả lời
Multiply each possible value by its probability and add: E(X) = ΣxP(X = x).
Thẻ 82
Câu hỏi
What does the standard deviation of a random variable measure?
Câu trả lời
The typical distance of long-run outcomes from the random variable's mean.
Thẻ 83
Câu hỏi
How is the standard deviation of a discrete random variable calculated?
Câu trả lời
σₓ = √[Σ(x − μₓ)²P(X = x)]. The quantity inside the square root is Var(X).
Thẻ 84
Câu hỏi
A game has E(X) = −$0.40 per play. What does this mean?
Câu trả lời
Over many plays, the player's average net result approaches a loss of 40 cents per play; it does not predict every play.
Thẻ 85
Câu hỏi
What conditions define a binomial random variable?
Câu trả lời
A fixed number of independent trials, two outcomes per trial, constant success probability, and X counts successes.
Thẻ 86
Câu hỏi
For X ~ Binomial(n, p), what are the mean and standard deviation?
Câu trả lời
Mean = np; standard deviation = √[np(1 − p)].
Thẻ 87
Câu hỏi
For X ~ Binomial(n, p), what is P(X = x)?
Câu trả lời
Choose x success positions, then multiply: C(n, x)pˣ(1 − p)ⁿ⁻ˣ.
Thẻ 88
Câu hỏi
How can P(X ≥ 1) be found efficiently for a binomial variable?
Câu trả lời
Use the complement: P(X ≥ 1) = 1 − P(X = 0).
Thẻ 89
Câu hỏi
What should one simulated trial represent when estimating P(X ≥ 4) for X ~ Binomial(10, 0.3)?
Câu trả lời
Ten independent success/failure observations with success probability 0.3, followed by recording whether at least four successes occurred.
Thẻ 90
Câu hỏi
What features characterize a normal distribution?
Câu trả lời
It is continuous, symmetric, unimodal, and bell-shaped.
Thẻ 91
Câu hỏi
Which parameters determine a normal distribution?
Câu trả lời
Its mean μ sets the center, and its standard deviation σ sets the spread.
Thẻ 92
Câu hỏi
What is the standard normal distribution?
Câu trả lời
The normal distribution with mean 0 and standard deviation 1.
Thẻ 93
Câu hỏi
What is the 68–95–99.7 rule?
Câu trả lời
For an approximately normal distribution, about 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations of the mean.
Thẻ 94
Câu hỏi
What does an area under a normal curve represent?
Câu trả lời
The probability or population proportion within the corresponding interval.
Thẻ 95
Câu hỏi
How do you find the value cutting off the lowest 10% of a normal distribution?
Câu trả lời
Find the z-score with cumulative area 0.10, then convert with x = μ + zσ.
Thẻ 96
Câu hỏi
A normal variable has μ = 50 and σ = 8. What z-score corresponds to x = 62?
Câu trả lời
1.5, because z = (62 − 50) / 8.
Thẻ 97
Câu hỏi
Two exam scores come from different normal distributions. What makes their percentiles comparable?
Câu trả lời
Standardize each score with its own distribution's mean and standard deviation, then compare z-scores or cumulative areas.
Thẻ 98
Câu hỏi
What is a sampling distribution of a statistic?
Câu trả lời
The distribution of that statistic over all possible random samples of a fixed size from a population.
Thẻ 99
Câu hỏi
How can a sampling distribution be approximated by simulation?
Câu trả lời
Repeatedly take random samples of the same size, calculate the statistic each time, and graph the resulting values.
Thẻ 100
Câu hỏi
What is a randomization distribution?
Câu trả lời
A simulated distribution of a statistic produced by repeatedly reallocating responses or labels as specified by a null model.
Thẻ 101
Câu hỏi
What does the central limit theorem say about sample means?
Câu trả lời
For random samples, the sampling distribution of the sample mean becomes approximately normal as sample size grows, even when the population is not normal.
Thẻ 102
Câu hỏi
How does increasing sample size affect the normal approximation in the central limit theorem?
Câu trả lời
It generally improves the approximation, especially for skewed or irregular populations.
Thẻ 103
Câu hỏi
A segmented bar chart shows nearly identical category proportions for every group. What does that suggest?
Câu trả lời
Little or no association between the two categorical variables.
Thẻ 104
Câu hỏi
In a survey, 30 of 120 students both bike to school and arrive before 8:00. What is the joint relative frequency?
Câu trả lời
0.25, because 30 / 120 = 0.25.
Thẻ 105
Câu hỏi
Why can P(A | B) differ from P(B | A)?
Câu trả lời
They use different restricted sample spaces and usually have different denominators.
Thẻ 106
Câu hỏi
If P(A) = 0.4 and P(A | B) = 0.4 with P(B) > 0, what does this indicate?
Câu trả lời
A and B are independent because learning B does not change the probability of A.
Thẻ 107
Câu hỏi
If independent events have probabilities 0.6 and 0.5, what is the probability that both occur?
Câu trả lời
0.30, using P(A ∩ B) = P(A)P(B).
Thẻ 108
Câu hỏi
A prize is $0 with probability 0.7 and $10 with probability 0.3. What is the expected prize?
Câu trả lời
$3, because 0(0.7) + 10(0.3) = 3.
Thẻ 109
Câu hỏi
A machine produces defective items independently with probability 0.02. What distribution models the number of defectives in 50 items?
Câu trả lời
Binomial with n = 50 and p = 0.02.
Thẻ 110
Câu hỏi
Heights are approximately normal with μ = 170 cm and σ = 6 cm. About what percent lie from 158 to 182 cm?
Câu trả lời
About 95%, because the interval is μ ± 2σ.
Thẻ 111
Câu hỏi
What makes an estimator unbiased?
Câu trả lời
Its sampling distribution is centered at the population parameter it estimates.
Thẻ 112
Câu hỏi
For random samples of size n, what is the mean of the sampling distribution of p̂?
Câu trả lời
μₚ̂ = p, where p is the population proportion.
Thẻ 113
Câu hỏi
Which procedure estimates one population proportion from a random sample?
Câu trả lời
A one-sample z-interval for a population proportion.
Thẻ 114
Câu hỏi
How should a confidence interval for a population proportion be interpreted?
Câu trả lời
We are confident at the stated level that the interval captures the true population proportion, in context.
Thẻ 115
Câu hỏi
What hypotheses test whether a population proportion differs from 0.40?
Câu trả lời
H₀: p = 0.40 versus Hₐ: p ≠ 0.40.
Thẻ 116
Câu hỏi
What is a p-value?
Câu trả lời
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.
Thẻ 117
Câu hỏi
What is the hypothesis-test decision rule using significance level α?
Câu trả lời
Reject H₀ when the p-value ≤ α; otherwise fail to reject H₀.
Thẻ 118
Câu hỏi
What is a Type I error?
Câu trả lời
Rejecting H₀ when H₀ is actually true.
Thẻ 119
Câu hỏi
What is the mean of p̂₁ − p̂₂ for independent random samples?
Câu trả lời
p₁ − p₂.
Thẻ 120
Câu hỏi
Which procedure estimates p₁ − p₂ from two independent samples or randomized groups?
Câu trả lời
A two-sample z-interval for a difference between population proportions.
Thẻ 121
Câu hỏi
How should a confidence interval for p₁ − p₂ be interpreted?
Câu trả lời
We are confident at the stated level that the interval captures the true difference p₁ − p₂, in context.
Thẻ 122
Câu hỏi
What null hypothesis is standard when testing whether two population proportions differ?
Câu trả lời
H₀: p₁ − p₂ = 0, equivalently p₁ = p₂.
Thẻ 123
Câu hỏi
A two-proportion test gives p-value 0.018 at α = 0.05. What decision follows?
Câu trả lời
Reject H₀ because 0.018 < 0.05.
Thẻ 124
Câu hỏi
When is a chi-square test for independence appropriate?
Câu trả lời
When one random sample provides two categorical variables and the question asks whether they are associated in one population.
Thẻ 125
Câu hỏi
How should a chi-square test p-value be interpreted?
Câu trả lời
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 thẻ
AP Statistics Flashcards: Complete 5-Unit Course Review
Học bộ thẻ này miễn phíNibomo sẽ mở ra để bạn bắt đầu học.
Thẻ 126
Câu hỏi
How do bias and variability differ for an estimator?
Câu trả lời
Bias concerns where the sampling distribution is centered; variability concerns how spread out it is.
Thẻ 127
Câu hỏi
What is the standard deviation of p̂ when observations are independent?
Câu trả lời
σₚ̂ = √[p(1 − p) / n].
Thẻ 128
Câu hỏi
What is the one-proportion z-interval formula?
Câu trả lời
p̂ ± z*√[p̂(1 − p̂) / n].
Thẻ 129
Câu hỏi
What does a 95% confidence level describe?
Câu trả lời
In repeated random sampling with the same method, about 95% of the resulting intervals would capture the true parameter.
Thẻ 130
Câu hỏi
Which method tests a claim about one population proportion when its conditions hold?
Câu trả lời
A one-sample z-test for a population proportion.
Thẻ 131
Câu hỏi
How does the alternative hypothesis determine a p-value's tail area?
Câu trả lời
A greater-than alternative uses the upper tail, a less-than alternative uses the lower tail, and a not-equal alternative uses both tails.
Thẻ 132
Câu hỏi
What wording should follow a rejected null hypothesis?
Câu trả lời
There is convincing statistical evidence for the alternative claim about the population parameter, stated in context.
Thẻ 133
Câu hỏi
What is a Type II error?
Câu trả lời
Failing to reject H₀ when Hₐ is actually true.
Thẻ 134
Câu hỏi
What is the standard deviation of p̂₁ − p̂₂ for independent samples?
Câu trả lời
√[p₁(1 − p₁)/n₁ + p₂(1 − p₂)/n₂].
Thẻ 135
Câu hỏi
What standard error is used in a confidence interval for p₁ − p₂?
Câu trả lời
√[p̂₁(1 − p̂₁)/n₁ + p̂₂(1 − p̂₂)/n₂]; the sample proportions are not pooled.
Thẻ 136
Câu hỏi
A confidence interval for p₁ − p₂ contains 0. What does that imply?
Câu trả lời
The interval does not provide convincing evidence of a difference between the population proportions at the corresponding two-sided significance level.
Thẻ 137
Câu hỏi
Why is a pooled proportion used in a two-proportion z-test with H₀: p₁ = p₂?
Câu trả lời
The null model assumes both samples share one common population proportion, estimated by combining successes and observations.
Thẻ 138
Câu hỏi
How should a p-value for a two-proportion test be stated?
Câu trả lời
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.
Thẻ 139
Câu hỏi
When is a chi-square test for homogeneity appropriate?
Câu trả lời
When independent samples or randomized groups are compared on the distribution of one categorical response variable.
Thẻ 140
Câu hỏi
What is the chi-square test statistic formula?
Câu trả lời
χ² = Σ[(observed − expected)² / expected], summed over all cells.
Thẻ 141
Câu hỏi
What usually happens to an estimator's sampling variability as sample size increases?
Câu trả lời
It decreases; estimates from larger random samples tend to cluster more tightly around the parameter.
Thẻ 142
Câu hỏi
When is the sampling distribution of p̂ approximately normal?
Câu trả lời
When the expected counts np and n(1 − p) are both at least 10.
Thẻ 143
Câu hỏi
What conditions justify a one-proportion z-interval?
Câu trả lời
Random data; independence, checked with n ≤ 10% of the population when sampling without replacement; and at least 10 observed successes and 10 observed failures.
Thẻ 144
Câu hỏi
A 95% confidence interval for p is (0.52, 0.61). What does it say about the claim p = 0.50?
Câu trả lời
The interval excludes 0.50, so the data provide evidence against p = 0.50 in a two-sided test at α = 0.05.
Thẻ 145
Câu hỏi
What is the one-proportion z-test statistic?
Câu trả lời
z = (p̂ − p₀) / √[p₀(1 − p₀)/n], using the null proportion p₀ in the standard error.
Thẻ 146
Câu hỏi
How is a simulation-based p-value estimated?
Câu trả lời
Find the proportion of simulated null statistics at least as extreme as the observed statistic in the direction of Hₐ.
Thẻ 147
Câu hỏi
What does “fail to reject H₀” mean?
Câu trả lời
The data do not provide convincing evidence for Hₐ; it does not prove H₀ true.
Thẻ 148
Câu hỏi
With sample size and effect fixed, what often happens when α is lowered?
Câu trả lời
The chance of a Type I error decreases, while the chance of a Type II error increases.
Thẻ 149
Câu hỏi
What conditions support the usual model for p̂₁ − p̂₂?
Câu trả lời
Independent random samples or randomized groups, independence within each group, and large enough expected success and failure counts for normal approximation.
Thẻ 150
Câu hỏi
What conditions justify a two-proportion z-interval?
Câu trả lời
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.
Thẻ 151
Câu hỏi
How does increasing both sample sizes affect a confidence interval for p₁ − p₂?
Câu trả lời
It reduces the standard error and usually narrows the interval when other factors stay the same.
Thẻ 152
Câu hỏi
What standard error is used in the two-proportion z-test?
Câu trả lời
√[p̂c(1 − p̂c)(1/n₁ + 1/n₂)], where p̂c is the pooled sample proportion.
Thẻ 153
Câu hỏi
A randomized experiment uses volunteers assigned to two treatments. A significant two-proportion test supports what scope?
Câu trả lời
A cause-and-effect conclusion for people similar to the volunteers, not automatic generalization to a broader population.
Thẻ 154
Câu hỏi
How is an expected count computed in a two-way table under independence?
Câu trả lời
Expected count = (row total × column total) / grand total.
Thẻ 155
Câu hỏi
What conditions justify a chi-square test for a two-way table?
Câu trả lời
Random data; independent observations, including the 10% check when sampling without replacement; and every expected cell count greater than 5.
Thẻ 156
Câu hỏi
A sampling distribution is centered away from the true parameter. What problem does this reveal?
Câu trả lời
Bias in the estimator.
Thẻ 157
Câu hỏi
If p = 0.30 and n = 100, what does μₚ̂ = 0.30 mean?
Câu trả lời
Across many random samples of 100, the average sample proportion would be 0.30.
Thẻ 158
Câu hỏi
For a planned proportion interval with margin of error m, what conservative p-value is used when no prior estimate exists?
Câu trả lời
Use p* = 0.50 in n ≥ (z*/m)²p*(1 − p*) because it gives the largest required sample size.
Thẻ 159
Câu hỏi
What two changes widen a confidence interval for a proportion?
Câu trả lời
Using a higher confidence level or a smaller sample size.
Thẻ 160
Câu hỏi
Which counts check normality for a one-proportion z-test?
Câu trả lời
Use the null model: np₀ ≥ 10 and n(1 − p₀) ≥ 10.
Thẻ 161
Câu hỏi
What is wrong with saying “the p-value is the probability that H₀ is true”?
Câu trả lời
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.
Thẻ 162
Câu hỏi
What does “statistically significant at α = 0.01” mean?
Câu trả lời
The p-value is at most 0.01, so H₀ is rejected at that significance level.
Thẻ 163
Câu hỏi
What is the power of a hypothesis test?
Câu trả lời
The probability that the test rejects H₀ when a particular alternative is true.
Thẻ 164
Câu hỏi
If p₁ = p₂, where is the sampling distribution of p̂₁ − p̂₂ centered?
Câu trả lời
At 0, because its mean is p₁ − p₂.
Thẻ 165
Câu hỏi
Why must the order p̂₁ − p̂₂ stay consistent throughout an interval?
Câu trả lời
Changing the order reverses the sign and changes the contextual interpretation of every endpoint.
Thẻ 166
Câu hỏi
A 95% interval for p₁ − p₂ is (0.04, 0.15). What conclusion is supported?
Câu trả lời
p₁ is plausibly 0.04 to 0.15 higher than p₂; the interval supports a positive difference.
Thẻ 167
Câu hỏi
Which success-failure counts are checked for a two-proportion z-test?
Câu trả lời
Expected counts based on the pooled null proportion: n₁p̂c, n₁(1 − p̂c), n₂p̂c, and n₂(1 − p̂c), each at least 10.
Thẻ 168
Câu hỏi
A two-proportion test with Hₐ: p₁ ≠ p₂ fails to reject H₀. What conclusion is valid?
Câu trả lời
There is not convincing evidence that the two population proportions differ.
Thẻ 169
Câu hỏi
What are the degrees of freedom for a chi-square test on an r × c table?
Câu trả lời
(r − 1)(c − 1).
Thẻ 170
Câu hỏi
A chi-square test for independence has a small p-value. What conclusion is appropriate?
Câu trả lời
There is convincing evidence of an association between the two categorical variables in the population, stated in context.
Thẻ 171
Câu hỏi
What is the mean of the sampling distribution of x̄ for random samples from a population with mean μ?
Câu trả lời
μₓ̄ = μ.
Thẻ 172
Câu hỏi
Which procedure estimates one population mean when the population standard deviation is unknown?
Câu trả lời
A one-sample t-interval for a population mean.
Thẻ 173
Câu hỏi
How should a confidence interval for a population mean be interpreted?
Câu trả lời
We are confident at the stated level that the interval captures the true population mean, in context.
Thẻ 174
Câu hỏi
What hypotheses test whether a population mean exceeds 12?
Câu trả lời
H₀: μ = 12 versus Hₐ: μ > 12.
Thẻ 175
Câu hỏi
A one-sample t-test gives p-value 0.08 at α = 0.05. What decision follows?
Câu trả lời
Fail to reject H₀ because 0.08 > 0.05.
Thẻ 176
Câu hỏi
What is the mean of x̄₁ − x̄₂ for independent random samples?
Câu trả lời
μ₁ − μ₂.
Thẻ 177
Câu hỏi
Which procedure estimates μ₁ − μ₂ from two independent samples?
Câu trả lời
A two-sample t-interval for a difference between population means.
Thẻ 178
Câu hỏi
How should a confidence interval for μ₁ − μ₂ be interpreted?
Câu trả lời
We are confident at the stated level that the interval captures the true difference μ₁ − μ₂, in context.
Thẻ 179
Câu hỏi
What null hypothesis is standard when testing whether two population means differ?
Câu trả lời
H₀: μ₁ − μ₂ = 0, equivalently μ₁ = μ₂.
Thẻ 180
Câu hỏi
A two-sample t-test gives p-value 0.004 at α = 0.01. What decision follows?
Câu trả lời
Reject H₀ because 0.004 < 0.01.
Thẻ 181
Câu hỏi
What is the standard deviation of x̄ when observations are independent?
Câu trả lời
σₓ̄ = σ / √n.
Thẻ 182
Câu hỏi
What is the one-sample t-interval formula for μ?
Câu trả lời
x̄ ± t* × s/√n, with t* based on n − 1 degrees of freedom.
Thẻ 183
Câu hỏi
What does a 90% confidence level mean for a mean interval procedure?
Câu trả lời
Across many random samples using the same procedure, about 90% of the intervals would capture the true population mean.
Thẻ 184
Câu hỏi
Which procedure tests a claim about one population mean when σ is unknown?
Câu trả lời
A one-sample t-test for a population mean.
Thẻ 185
Câu hỏi
How should a one-mean test p-value be interpreted?
Câu trả lời
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.
Thẻ 186
Câu hỏi
What is the standard deviation of x̄₁ − x̄₂ for independent samples?
Câu trả lời
√(σ₁²/n₁ + σ₂²/n₂).
Thẻ 187
Câu hỏi
What standard error is used in a two-sample t-interval for μ₁ − μ₂?
Câu trả lời
√(s₁²/n₁ + s₂²/n₂).
Thẻ 188
Câu hỏi
A confidence interval for μ₁ − μ₂ contains 0. What does that imply?
Câu trả lời
The interval does not provide convincing evidence of a difference between the population means at the corresponding two-sided significance level.
Thẻ 189
Câu hỏi
What is the two-sample t-statistic for testing H₀: μ₁ − μ₂ = 0?
Câu trả lời
t = [(x̄₁ − x̄₂) − 0] / √(s₁²/n₁ + s₂²/n₂).
Thẻ 190
Câu hỏi
How should a two-mean test p-value be interpreted?
Câu trả lời
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.
Thẻ 191
Câu hỏi
When is the sampling distribution of x̄ approximately normal?
Câu trả lời
When the population is approximately normal or the random sample is large enough for the central limit theorem to apply.
Thẻ 192
Câu hỏi
What conditions justify a one-sample t-interval?
Câu trả lời
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.
Thẻ 193
Câu hỏi
How does increasing sample size affect a confidence interval for μ?
Câu trả lời
It lowers the standard error and usually narrows the interval when confidence level and variability stay comparable.
Thẻ 194
Câu hỏi
What is the one-sample t-test statistic?
Câu trả lời
t = (x̄ − μ₀) / (s/√n), with n − 1 degrees of freedom.
Thẻ 195
Câu hỏi
A t-test fails to reject H₀. What should the conclusion avoid?
Câu trả lời
Avoid saying H₀ is true; say the data do not provide convincing evidence for Hₐ.
Thẻ 196
Câu hỏi
When is x̄₁ − x̄₂ approximately normal?
Câu trả lời
When both populations are approximately normal or both independent random samples are large enough for normal approximations.
Thẻ 197
Câu hỏi
What conditions justify a two-sample t-interval?
Câu trả lời
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.
Thẻ 198
Câu hỏi
A 95% interval for μ₁ − μ₂ is (−7.2, −1.4). What does it support?
Câu trả lời
μ₁ is plausibly 1.4 to 7.2 units lower than μ₂; the interval supports a negative difference.
Thẻ 199
Câu hỏi
What sample-shape condition is checked for a two-sample t-test with small samples?
Câu trả lời
Both sample distributions should be free of strong skewness and outliers unless both populations are known to be approximately normal.
Thẻ 200
Câu hỏi
A randomized experiment finds a significant difference in mean response. What can random assignment support?
Câu trả lời
A cause-and-effect conclusion for units like those studied, assuming the experiment was well designed.
Thẻ 201
Câu hỏi
A population has μ = 40. What does μₓ̄ = 40 mean for samples of size 25?
Câu trả lời
Across all random samples of 25, the average sample mean is 40.
Thẻ 202
Câu hỏi
How is a matched-pairs confidence interval analyzed?
Câu trả lời
Compute one difference for each pair, then use a one-sample t-interval on the population mean difference.
Thẻ 203
Câu hỏi
A 95% confidence interval for μ is (18.2, 21.7). What does it say about μ = 22?
Câu trả lời
The interval excludes 22, providing evidence against μ = 22 in a two-sided test at α = 0.05.
Thẻ 204
Câu hỏi
Which observations enter a matched-pairs t-test?
Câu trả lời
The within-pair differences, not the two original columns treated as independent samples.
Thẻ 205
Câu hỏi
A test reports p-value 0.032. At which common levels is it significant: 0.05 or 0.01?
Câu trả lời
Significant at 0.05, but not at 0.01.
Thẻ 206
Câu hỏi
If μ₁ − μ₂ = 5, where is the sampling distribution of x̄₁ − x̄₂ centered?
Câu trả lời
At 5.
Thẻ 207
Câu hỏi
Does the standard AP two-sample t procedure require equal population variances?
Câu trả lời
No. It uses separate sample variances in the standard error rather than pooling them.
Thẻ 208
Câu hỏi
What two changes usually widen a confidence interval for μ₁ − μ₂?
Câu trả lời
Higher confidence or smaller sample sizes.
Thẻ 209
Câu hỏi
Why must the order x̄₁ − x̄₂ match the order μ₁ − μ₂ in the hypotheses?
Câu trả lời
Reversing the order reverses the sign and changes the direction of the claim.
Thẻ 210
Câu hỏi
A two-sample test with Hₐ: μ₁ > μ₂ fails to reject H₀. What conclusion is valid?
Câu trả lời
There is not convincing evidence that μ₁ exceeds μ₂.
Thẻ 211
Câu hỏi
A population has σ = 18 and random samples have n = 36. What is σₓ̄?
Câu trả lời
3, because 18/√36 = 3.
Thẻ 212
Câu hỏi
Why is a t distribution used for inference about a mean when σ is unknown?
Câu trả lời
Replacing σ with the sample standard deviation s adds uncertainty, which the heavier-tailed t distribution accounts for.
Thẻ 213
Câu hỏi
What conditions justify a one-sample t-test?
Câu trả lời
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.
Thẻ 214
Câu hỏi
What distinguishes a two-sample means procedure from a matched-pairs procedure?
Câu trả lời
Two-sample procedures use independent groups; matched-pairs procedures analyze linked observations through their differences.
Thẻ 215
Câu hỏi
How are degrees of freedom handled for a two-sample t procedure?
Câu trả lời
Technology usually uses an approximation based on both sample variances and sizes; a conservative fallback uses the smaller of n₁ − 1 and n₂ − 1.
Thẻ 216
Câu hỏi
What type of variables belong on a scatterplot?
Câu trả lời
Two quantitative variables measured on the same observational units.
Thẻ 217
Câu hỏi
What does the correlation coefficient r describe?
Câu trả lời
The direction and strength of a linear relationship between two quantitative variables.
Thẻ 218
Câu hỏi
What does ŷ = a + bx represent?
Câu trả lời
A linear regression model predicting response y from explanatory variable x.
Thẻ 219
Câu hỏi
What is a residual?
Câu trả lời
Observed response minus predicted response: residual = y − ŷ.
Thẻ 220
Câu hỏi
What makes a regression line the least-squares line?
Câu trả lời
It minimizes the sum of squared residuals.
Thẻ 221
Câu hỏi
What four features should a scatterplot description address?
Câu trả lời
Direction, form, strength, and unusual features such as outliers or clusters.
Thẻ 222
Câu hỏi
What values can r take?
Câu trả lời
Any value from −1 to 1, inclusive.
Thẻ 223
Câu hỏi
How is the slope b interpreted in context?
Câu trả lời
For each one-unit increase in x, the predicted value of y changes by b units on average.
Thẻ 224
Câu hỏi
What does a positive residual mean?
Câu trả lời
The observed response is above the model's predicted response.
Thẻ 225
Câu hỏi
What is the least-squares slope formula?
Câu trả lời
b = r(sᵧ/sₓ).
Thẻ 226
Câu hỏi
A scatterplot trends downward from left to right. What direction is the association?
Câu trả lời
Negative: larger x-values tend to occur with smaller y-values.
Thẻ 227
Câu hỏi
Why can r be near 0 even when two variables are strongly related?
Câu trả lời
Correlation measures only linear association, so a strong curved relationship can have r near 0.
Thẻ 228
Câu hỏi
How is the intercept a interpreted in context?
Câu trả lời
It is the predicted response when x = 0, provided x = 0 is meaningful and within the data's scope.
Thẻ 229
Câu hỏi
A model predicts 18, and the observed response is 21. What is the residual?
Câu trả lời
3, because 21 − 18 = 3.
Thẻ 230
Câu hỏi
How is the least-squares intercept found from the slope?
Câu trả lời
a = ȳ − bx̄.
Thẻ 231
Câu hỏi
What makes a linear association look strong?
Câu trả lời
The points lie close to a straight-line pattern, regardless of whether the slope is steep or shallow.
Thẻ 232
Câu hỏi
Does r have measurement units?
Câu trả lời
No. Correlation is unitless because it is based on standardized values.
Thẻ 233
Câu hỏi
For ŷ = 12 + 2.5x, what is predicted when x = 4?
Câu trả lời
22, because 12 + 2.5(4) = 22.
Thẻ 234
Câu hỏi
What residual-plot pattern supports using a linear model?
Câu trả lời
Random scatter around zero with no clear curve, trend, or changing spread.
Thẻ 235
Câu hỏi
What does r² measure in simple linear regression?
Câu trả lời
The proportion of variation in the response variable explained by its linear relationship with the explanatory variable.
Thẻ 236
Câu hỏi
A scatterplot shows a strong association. Does that establish causation?
Câu trả lời
No. A scatterplot alone cannot rule out confounding or other explanations.
Thẻ 237
Câu hỏi
Why should unusual points be checked before interpreting r?
Câu trả lời
Correlation is not resistant; an outlier or influential point can change r substantially.
Thẻ 238
Câu hỏi
Why is extrapolation risky?
Câu trả lời
The relationship observed over the data range may not continue beyond that range.
Thẻ 239
Câu hỏi
A point lies below the regression line. What sign is its residual?
Câu trả lời
Negative, because observed y is less than predicted ŷ.
Thẻ 240
Câu hỏi
Which point always lies on a least-squares regression line with an intercept?
Câu trả lời
The point (x̄, ȳ).
Thẻ 241
Câu hỏi
Which variable goes on each axis of a scatterplot used for prediction?
Câu trả lời
The explanatory variable goes on the horizontal x-axis; the response variable goes on the vertical y-axis.
Thẻ 242
Câu hỏi
What happens to r if the roles of x and y are swapped?
Câu trả lời
Nothing. Correlation is symmetric.
Thẻ 243
Câu hỏi
What is interpolation?
Câu trả lời
Predicting a response for an x-value within the range of observed explanatory values.
Thẻ 244
Câu hỏi
A residual plot has a clear U-shape. What is the correction?
Câu trả lời
Do not treat the linear model as adequate; the curved pattern shows systematic structure remains.
Thẻ 245
Câu hỏi
A regression has r² = 0.64. What does this mean?
Câu trả lời
About 64% of the variation in the response is explained by its linear relationship with the explanatory variable.
Thẻ 246
Câu hỏi
What is an outlier in a scatterplot?
Câu trả lời
A point that falls away from the overall pattern of the other points.
Thẻ 247
Câu hỏi
What happens to r when x is converted from centimeters to meters?
Câu trả lời
It stays the same because multiplying by a positive constant does not change standardized linear association.
Thẻ 248
Câu hỏi
When can a regression relationship support a causal conclusion?
Câu trả lời
Only when the data come from a well-designed randomized experiment and the conclusion matches its scope.
Thẻ 249
Câu hỏi
What units does a residual use?
Câu trả lời
The same units as the response variable y.
Thẻ 250
Câu hỏi
What is an influential point in regression?
Câu trả lời
A point whose removal substantially changes the fitted regression line or another key regression result.
250 thẻ
AP Statistics Flashcards: Complete 5-Unit Course Review
Nibomo sẽ mở ra để bạn bắt đầu học.