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