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 aquesta baralla
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.
Targetes d'aquesta baralla
Targeta 1
Pregunta
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.
Targeta 2
Pregunta
What is an observational unit?
Resposta
An individual item or person from which data are collected.
Targeta 3
Pregunta
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.
Targeta 4
Pregunta
How does a parameter differ from a statistic?
Resposta
A parameter describes a population; a statistic describes a sample.
Targeta 5
Pregunta
How is a category's relative frequency calculated?
Resposta
Divide the category count by the total number of observations.
Targeta 6
Pregunta
What should the height of a bar represent in a relative-frequency bar chart?
Resposta
The proportion or percentage of observations in that category.
Targeta 7
Pregunta
Number of text messages sent in a day: discrete or continuous?
Resposta
Discrete. It is a count with separated possible values.
Targeta 8
Pregunta
Which displays preserve individual quantitative data values?
Resposta
Dotplots and stem-and-leaf plots. A histogram groups values into intervals.
Targeta 9
Pregunta
What four features should a description of a quantitative distribution address?
Resposta
Shape, center, variability, and unusual features such as gaps or outliers.
Targeta 10
Pregunta
Which measure of center is usually better for a strongly right-skewed distribution?
Resposta
The median, because it is resistant to extreme high values.
Targeta 11
Pregunta
The values are 3, 5, 5, and 11. What is the mean?
Resposta
- The sum is 24, divided by 4 observations.
Targeta 12
Pregunta
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.
Targeta 13
Pregunta
How is the interquartile range calculated?
Resposta
IQR = Q3 − Q1. It measures the spread of the middle 50% of the data.
Targeta 14
Pregunta
What does a small standard deviation say about a data set?
Resposta
Values typically lie close to the mean.
Targeta 15
Pregunta
Which common summaries are resistant to extreme values?
Resposta
The median and IQR are resistant; the mean and standard deviation are not.
Targeta 16
Pregunta
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.
Targeta 17
Pregunta
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.
Targeta 18
Pregunta
How should two quantitative distributions be compared?
Resposta
Compare shape, center, variability, and unusual features in context, using the same measure or display basis.
Targeta 19
Pregunta
What does a z-score of −1.8 mean?
Resposta
The value is 1.8 standard deviations below the mean.
Targeta 20
Pregunta
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.
Targeta 21
Pregunta
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.
Targeta 22
Pregunta
What is a census?
Resposta
A study that collects data from every member of the population.
Targeta 23
Pregunta
What makes a study an experiment?
Resposta
Researchers deliberately assign treatments to experimental units.
Targeta 24
Pregunta
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.
Targeta 25
Pregunta
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.
Targeta 26
Pregunta
What study feature supports generalizing results to a population?
Resposta
Random selection from that population.
Targeta 27
Pregunta
What makes a study observational?
Resposta
Researchers observe variables without assigning treatments.
Targeta 28
Pregunta
What study feature supports a cause-and-effect conclusion?
Resposta
Random assignment of treatments in a well-designed experiment.
Targeta 29
Pregunta
What defines a simple random sample of size n?
Resposta
Every possible sample of size n has the same chance of selection.
Targeta 30
Pregunta
What changes when sampling is done with replacement?
Resposta
A selected unit returns to the population and can be selected again.
Targeta 31
Pregunta
Why can a convenience sample be biased?
Resposta
Easy-to-reach units may differ systematically from the target population.
Targeta 32
Pregunta
Why should an experiment compare at least two treatment groups?
Resposta
The comparison provides a baseline for judging whether responses differ by treatment.
Targeta 33
Pregunta
A school samples 20 students at random from each grade. Which sampling method is this?
Resposta
Stratified random sampling, with grade as the stratum.
Targeta 34
Pregunta
What is the purpose of random assignment?
Resposta
It tends to balance lurking variables across treatment groups, supporting causal inference.
Targeta 35
Pregunta
Why can a voluntary-response sample be biased?
Resposta
People with strong opinions are often more likely to participate.
Targeta 36
Pregunta
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.
Targeta 37
Pregunta
A city randomly selects 8 apartment buildings and surveys every household in those buildings. Which method is this?
Resposta
Cluster random sampling.
Targeta 38
Pregunta
What does direct control do in an experiment?
Resposta
It holds potential extraneous sources of variation constant across experimental units.
Targeta 39
Pregunta
What is undercoverage?
Resposta
Some groups in the target population are left out of, or poorly represented in, the sampling frame.
Targeta 40
Pregunta
What is the role of a control group?
Resposta
It supplies a comparison condition for evaluating the treatment of interest.
Targeta 41
Pregunta
After a random start, a quality inspector checks every 40th item. Which sampling method is this?
Resposta
Systematic random sampling.
Targeta 42
Pregunta
Why might an experiment use a placebo?
Resposta
To separate a treatment's effect from responses caused by expecting treatment.
Targeta 43
Pregunta
What is nonresponse bias?
Resposta
Selected individuals who do not respond differ in a relevant way from those who do.
Targeta 44
Pregunta
What is single blinding designed to reduce?
Resposta
Bias caused when participants or evaluators know which treatment was received, depending on who is blinded.
Targeta 45
Pregunta
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.
Targeta 46
Pregunta
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.
Targeta 47
Pregunta
A survey asks, “Don't you agree the new schedule is unfair?” What problem does this create?
Resposta
Response bias from leading wording.
Targeta 48
Pregunta
What usually makes an experiment double-blind?
Resposta
Neither the participants nor the people evaluating responses know treatment assignments while outcomes are measured.
Targeta 49
Pregunta
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.
Targeta 50
Pregunta
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.
Targeta 51
Pregunta
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.
Targeta 52
Pregunta
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.
Targeta 53
Pregunta
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.
Targeta 54
Pregunta
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.
Targeta 55
Pregunta
What does it mean that a score is at the 80th percentile?
Resposta
About 80% of scores are at or below it.
Targeta 56
Pregunta
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.
Targeta 57
Pregunta
What is the minimum ethical safeguard when collecting identifiable human data?
Resposta
Obtain informed consent when required and protect participants' privacy and confidentiality.
Targeta 58
Pregunta
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.
Targeta 59
Pregunta
A study uses random sampling but no assigned treatment. What can it support?
Resposta
Population generalization, but not a cause-and-effect conclusion.
Targeta 60
Pregunta
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.
Targeta 61
Pregunta
What does a two-way table summarize?
Resposta
Counts or relative frequencies for combinations of two categorical variables.
Targeta 62
Pregunta
What is a joint relative frequency?
Resposta
A cell count divided by the grand total, representing one combination of categories.
Targeta 63
Pregunta
What is a marginal relative frequency?
Resposta
A row or column total divided by the grand total.
Targeta 64
Pregunta
How is a conditional relative frequency calculated within one row?
Resposta
Divide each cell in that row by the row total.
Targeta 65
Pregunta
What pattern suggests association between two categorical variables?
Resposta
The conditional distribution of one variable changes across categories of the other.
Targeta 66
Pregunta
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.
Targeta 67
Pregunta
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.
Targeta 68
Pregunta
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.
Targeta 69
Pregunta
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.
Targeta 70
Pregunta
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.
Targeta 71
Pregunta
What is the complement rule?
Resposta
P(Aᶜ) = 1 − P(A). It is often useful for “at least one” events.
Targeta 72
Pregunta
How can you verify that events A and B are mutually exclusive?
Resposta
Their intersection is impossible, so P(A ∩ B) = 0.
Targeta 73
Pregunta
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.
Targeta 74
Pregunta
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).
Targeta 75
Pregunta
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.
Targeta 76
Pregunta
What is the general addition rule?
Resposta
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Targeta 77
Pregunta
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.
Targeta 78
Pregunta
What is a random variable?
Resposta
A numerical value determined by the outcome of a random process.
Targeta 79
Pregunta
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.
Targeta 80
Pregunta
What does a cumulative distribution value F(x) represent?
Resposta
P(X ≤ x), the probability that the random variable is at most x.
Targeta 81
Pregunta
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).
Targeta 82
Pregunta
What does the standard deviation of a random variable measure?
Resposta
The typical distance of long-run outcomes from the random variable's mean.
Targeta 83
Pregunta
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).
Targeta 84
Pregunta
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.
Targeta 85
Pregunta
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.
Targeta 86
Pregunta
For X ~ Binomial(n, p), what are the mean and standard deviation?
Resposta
Mean = np; standard deviation = √[np(1 − p)].
Targeta 87
Pregunta
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.
Targeta 88
Pregunta
How can P(X ≥ 1) be found efficiently for a binomial variable?
Resposta
Use the complement: P(X ≥ 1) = 1 − P(X = 0).
Targeta 89
Pregunta
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.
Targeta 90
Pregunta
What features characterize a normal distribution?
Resposta
It is continuous, symmetric, unimodal, and bell-shaped.
Targeta 91
Pregunta
Which parameters determine a normal distribution?
Resposta
Its mean μ sets the center, and its standard deviation σ sets the spread.
Targeta 92
Pregunta
What is the standard normal distribution?
Resposta
The normal distribution with mean 0 and standard deviation 1.
Targeta 93
Pregunta
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.
Targeta 94
Pregunta
What does an area under a normal curve represent?
Resposta
The probability or population proportion within the corresponding interval.
Targeta 95
Pregunta
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.
Targeta 96
Pregunta
A normal variable has μ = 50 and σ = 8. What z-score corresponds to x = 62?
Resposta
1.5, because z = (62 − 50) / 8.
Targeta 97
Pregunta
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.
Targeta 98
Pregunta
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.
Targeta 99
Pregunta
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.
Targeta 100
Pregunta
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.
Targeta 101
Pregunta
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.
Targeta 102
Pregunta
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.
Targeta 103
Pregunta
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.
Targeta 104
Pregunta
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.
Targeta 105
Pregunta
Why can P(A | B) differ from P(B | A)?
Resposta
They use different restricted sample spaces and usually have different denominators.
Targeta 106
Pregunta
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.
Targeta 107
Pregunta
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).
Targeta 108
Pregunta
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.
Targeta 109
Pregunta
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.
Targeta 110
Pregunta
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.
Targeta 111
Pregunta
What makes an estimator unbiased?
Resposta
Its sampling distribution is centered at the population parameter it estimates.
Targeta 112
Pregunta
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.
Targeta 113
Pregunta
Which procedure estimates one population proportion from a random sample?
Resposta
A one-sample z-interval for a population proportion.
Targeta 114
Pregunta
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.
Targeta 115
Pregunta
What hypotheses test whether a population proportion differs from 0.40?
Resposta
H₀: p = 0.40 versus Hₐ: p ≠ 0.40.
Targeta 116
Pregunta
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.
Targeta 117
Pregunta
What is the hypothesis-test decision rule using significance level α?
Resposta
Reject H₀ when the p-value ≤ α; otherwise fail to reject H₀.
Targeta 118
Pregunta
What is a Type I error?
Resposta
Rejecting H₀ when H₀ is actually true.
Targeta 119
Pregunta
What is the mean of p̂₁ − p̂₂ for independent random samples?
Resposta
p₁ − p₂.
Targeta 120
Pregunta
Which procedure estimates p₁ − p₂ from two independent samples or randomized groups?
Resposta
A two-sample z-interval for a difference between population proportions.
Targeta 121
Pregunta
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.
Targeta 122
Pregunta
What null hypothesis is standard when testing whether two population proportions differ?
Resposta
H₀: p₁ − p₂ = 0, equivalently p₁ = p₂.
Targeta 123
Pregunta
A two-proportion test gives p-value 0.018 at α = 0.05. What decision follows?
Resposta
Reject H₀ because 0.018 < 0.05.
Targeta 124
Pregunta
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.
Targeta 125
Pregunta
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 targetes
AP Statistics Flashcards: Complete 5-Unit Course Review
Estudia aquesta baralla de francNibomo s'obre perquè puguis començar a estudiar.
Targeta 126
Pregunta
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.
Targeta 127
Pregunta
What is the standard deviation of p̂ when observations are independent?
Resposta
σₚ̂ = √[p(1 − p) / n].
Targeta 128
Pregunta
What is the one-proportion z-interval formula?
Resposta
p̂ ± z*√[p̂(1 − p̂) / n].
Targeta 129
Pregunta
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.
Targeta 130
Pregunta
Which method tests a claim about one population proportion when its conditions hold?
Resposta
A one-sample z-test for a population proportion.
Targeta 131
Pregunta
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.
Targeta 132
Pregunta
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.
Targeta 133
Pregunta
What is a Type II error?
Resposta
Failing to reject H₀ when Hₐ is actually true.
Targeta 134
Pregunta
What is the standard deviation of p̂₁ − p̂₂ for independent samples?
Resposta
√[p₁(1 − p₁)/n₁ + p₂(1 − p₂)/n₂].
Targeta 135
Pregunta
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.
Targeta 136
Pregunta
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.
Targeta 137
Pregunta
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.
Targeta 138
Pregunta
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.
Targeta 139
Pregunta
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.
Targeta 140
Pregunta
What is the chi-square test statistic formula?
Resposta
χ² = Σ[(observed − expected)² / expected], summed over all cells.
Targeta 141
Pregunta
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.
Targeta 142
Pregunta
When is the sampling distribution of p̂ approximately normal?
Resposta
When the expected counts np and n(1 − p) are both at least 10.
Targeta 143
Pregunta
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.
Targeta 144
Pregunta
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.
Targeta 145
Pregunta
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.
Targeta 146
Pregunta
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.
Targeta 147
Pregunta
What does “fail to reject H₀” mean?
Resposta
The data do not provide convincing evidence for Hₐ; it does not prove H₀ true.
Targeta 148
Pregunta
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.
Targeta 149
Pregunta
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.
Targeta 150
Pregunta
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.
Targeta 151
Pregunta
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.
Targeta 152
Pregunta
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.
Targeta 153
Pregunta
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.
Targeta 154
Pregunta
How is an expected count computed in a two-way table under independence?
Resposta
Expected count = (row total × column total) / grand total.
Targeta 155
Pregunta
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.
Targeta 156
Pregunta
A sampling distribution is centered away from the true parameter. What problem does this reveal?
Resposta
Bias in the estimator.
Targeta 157
Pregunta
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.
Targeta 158
Pregunta
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.
Targeta 159
Pregunta
What two changes widen a confidence interval for a proportion?
Resposta
Using a higher confidence level or a smaller sample size.
Targeta 160
Pregunta
Which counts check normality for a one-proportion z-test?
Resposta
Use the null model: np₀ ≥ 10 and n(1 − p₀) ≥ 10.
Targeta 161
Pregunta
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.
Targeta 162
Pregunta
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.
Targeta 163
Pregunta
What is the power of a hypothesis test?
Resposta
The probability that the test rejects H₀ when a particular alternative is true.
Targeta 164
Pregunta
If p₁ = p₂, where is the sampling distribution of p̂₁ − p̂₂ centered?
Resposta
At 0, because its mean is p₁ − p₂.
Targeta 165
Pregunta
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.
Targeta 166
Pregunta
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.
Targeta 167
Pregunta
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.
Targeta 168
Pregunta
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.
Targeta 169
Pregunta
What are the degrees of freedom for a chi-square test on an r × c table?
Resposta
(r − 1)(c − 1).
Targeta 170
Pregunta
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.
Targeta 171
Pregunta
What is the mean of the sampling distribution of x̄ for random samples from a population with mean μ?
Resposta
μₓ̄ = μ.
Targeta 172
Pregunta
Which procedure estimates one population mean when the population standard deviation is unknown?
Resposta
A one-sample t-interval for a population mean.
Targeta 173
Pregunta
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.
Targeta 174
Pregunta
What hypotheses test whether a population mean exceeds 12?
Resposta
H₀: μ = 12 versus Hₐ: μ > 12.
Targeta 175
Pregunta
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.
Targeta 176
Pregunta
What is the mean of x̄₁ − x̄₂ for independent random samples?
Resposta
μ₁ − μ₂.
Targeta 177
Pregunta
Which procedure estimates μ₁ − μ₂ from two independent samples?
Resposta
A two-sample t-interval for a difference between population means.
Targeta 178
Pregunta
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.
Targeta 179
Pregunta
What null hypothesis is standard when testing whether two population means differ?
Resposta
H₀: μ₁ − μ₂ = 0, equivalently μ₁ = μ₂.
Targeta 180
Pregunta
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.
Targeta 181
Pregunta
What is the standard deviation of x̄ when observations are independent?
Resposta
σₓ̄ = σ / √n.
Targeta 182
Pregunta
What is the one-sample t-interval formula for μ?
Resposta
x̄ ± t* × s/√n, with t* based on n − 1 degrees of freedom.
Targeta 183
Pregunta
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.
Targeta 184
Pregunta
Which procedure tests a claim about one population mean when σ is unknown?
Resposta
A one-sample t-test for a population mean.
Targeta 185
Pregunta
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.
Targeta 186
Pregunta
What is the standard deviation of x̄₁ − x̄₂ for independent samples?
Resposta
√(σ₁²/n₁ + σ₂²/n₂).
Targeta 187
Pregunta
What standard error is used in a two-sample t-interval for μ₁ − μ₂?
Resposta
√(s₁²/n₁ + s₂²/n₂).
Targeta 188
Pregunta
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.
Targeta 189
Pregunta
What is the two-sample t-statistic for testing H₀: μ₁ − μ₂ = 0?
Resposta
t = [(x̄₁ − x̄₂) − 0] / √(s₁²/n₁ + s₂²/n₂).
Targeta 190
Pregunta
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.
Targeta 191
Pregunta
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.
Targeta 192
Pregunta
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.
Targeta 193
Pregunta
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.
Targeta 194
Pregunta
What is the one-sample t-test statistic?
Resposta
t = (x̄ − μ₀) / (s/√n), with n − 1 degrees of freedom.
Targeta 195
Pregunta
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.
Targeta 196
Pregunta
When is x̄₁ − x̄₂ approximately normal?
Resposta
When both populations are approximately normal or both independent random samples are large enough for normal approximations.
Targeta 197
Pregunta
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.
Targeta 198
Pregunta
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.
Targeta 199
Pregunta
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.
Targeta 200
Pregunta
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.
Targeta 201
Pregunta
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.
Targeta 202
Pregunta
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.
Targeta 203
Pregunta
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.
Targeta 204
Pregunta
Which observations enter a matched-pairs t-test?
Resposta
The within-pair differences, not the two original columns treated as independent samples.
Targeta 205
Pregunta
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.
Targeta 206
Pregunta
If μ₁ − μ₂ = 5, where is the sampling distribution of x̄₁ − x̄₂ centered?
Resposta
At 5.
Targeta 207
Pregunta
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.
Targeta 208
Pregunta
What two changes usually widen a confidence interval for μ₁ − μ₂?
Resposta
Higher confidence or smaller sample sizes.
Targeta 209
Pregunta
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.
Targeta 210
Pregunta
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.
Targeta 211
Pregunta
A population has σ = 18 and random samples have n = 36. What is σₓ̄?
Resposta
3, because 18/√36 = 3.
Targeta 212
Pregunta
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.
Targeta 213
Pregunta
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.
Targeta 214
Pregunta
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.
Targeta 215
Pregunta
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.
Targeta 216
Pregunta
What type of variables belong on a scatterplot?
Resposta
Two quantitative variables measured on the same observational units.
Targeta 217
Pregunta
What does the correlation coefficient r describe?
Resposta
The direction and strength of a linear relationship between two quantitative variables.
Targeta 218
Pregunta
What does ŷ = a + bx represent?
Resposta
A linear regression model predicting response y from explanatory variable x.
Targeta 219
Pregunta
What is a residual?
Resposta
Observed response minus predicted response: residual = y − ŷ.
Targeta 220
Pregunta
What makes a regression line the least-squares line?
Resposta
It minimizes the sum of squared residuals.
Targeta 221
Pregunta
What four features should a scatterplot description address?
Resposta
Direction, form, strength, and unusual features such as outliers or clusters.
Targeta 222
Pregunta
What values can r take?
Resposta
Any value from −1 to 1, inclusive.
Targeta 223
Pregunta
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.
Targeta 224
Pregunta
What does a positive residual mean?
Resposta
The observed response is above the model's predicted response.
Targeta 225
Pregunta
What is the least-squares slope formula?
Resposta
b = r(sᵧ/sₓ).
Targeta 226
Pregunta
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.
Targeta 227
Pregunta
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.
Targeta 228
Pregunta
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.
Targeta 229
Pregunta
A model predicts 18, and the observed response is 21. What is the residual?
Resposta
3, because 21 − 18 = 3.
Targeta 230
Pregunta
How is the least-squares intercept found from the slope?
Resposta
a = ȳ − bx̄.
Targeta 231
Pregunta
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.
Targeta 232
Pregunta
Does r have measurement units?
Resposta
No. Correlation is unitless because it is based on standardized values.
Targeta 233
Pregunta
For ŷ = 12 + 2.5x, what is predicted when x = 4?
Resposta
22, because 12 + 2.5(4) = 22.
Targeta 234
Pregunta
What residual-plot pattern supports using a linear model?
Resposta
Random scatter around zero with no clear curve, trend, or changing spread.
Targeta 235
Pregunta
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.
Targeta 236
Pregunta
A scatterplot shows a strong association. Does that establish causation?
Resposta
No. A scatterplot alone cannot rule out confounding or other explanations.
Targeta 237
Pregunta
Why should unusual points be checked before interpreting r?
Resposta
Correlation is not resistant; an outlier or influential point can change r substantially.
Targeta 238
Pregunta
Why is extrapolation risky?
Resposta
The relationship observed over the data range may not continue beyond that range.
Targeta 239
Pregunta
A point lies below the regression line. What sign is its residual?
Resposta
Negative, because observed y is less than predicted ŷ.
Targeta 240
Pregunta
Which point always lies on a least-squares regression line with an intercept?
Resposta
The point (x̄, ȳ).
Targeta 241
Pregunta
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.
Targeta 242
Pregunta
What happens to r if the roles of x and y are swapped?
Resposta
Nothing. Correlation is symmetric.
Targeta 243
Pregunta
What is interpolation?
Resposta
Predicting a response for an x-value within the range of observed explanatory values.
Targeta 244
Pregunta
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.
Targeta 245
Pregunta
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.
Targeta 246
Pregunta
What is an outlier in a scatterplot?
Resposta
A point that falls away from the overall pattern of the other points.
Targeta 247
Pregunta
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.
Targeta 248
Pregunta
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.
Targeta 249
Pregunta
What units does a residual use?
Resposta
The same units as the response variable y.
Targeta 250
Pregunta
What is an influential point in regression?
Resposta
A point whose removal substantially changes the fitted regression line or another key regression result.
250 targetes
AP Statistics Flashcards: Complete 5-Unit Course Review
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