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