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