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