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