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