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