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.
دربارهٔ این دسته
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.
کارتهای این دسته
کارت ۱
پرسش
What makes a question a statistical investigative question?
پاسخ
It anticipates variability in data and can be answered by collecting and analyzing data about a population or process.
کارت ۲
پرسش
What is an observational unit?
پاسخ
An individual item or person from which data are collected.
کارت ۳
پرسش
A student's class year is recorded as freshman, sophomore, junior, or senior. What type of variable is this?
پاسخ
Categorical. The values name groups rather than measure a numerical amount.
کارت ۴
پرسش
How does a parameter differ from a statistic?
پاسخ
A parameter describes a population; a statistic describes a sample.
کارت ۵
پرسش
How is a category's relative frequency calculated?
پاسخ
Divide the category count by the total number of observations.
کارت ۶
پرسش
What should the height of a bar represent in a relative-frequency bar chart?
پاسخ
The proportion or percentage of observations in that category.
کارت ۷
پرسش
Number of text messages sent in a day: discrete or continuous?
پاسخ
Discrete. It is a count with separated possible values.
کارت ۸
پرسش
Which displays preserve individual quantitative data values?
پاسخ
Dotplots and stem-and-leaf plots. A histogram groups values into intervals.
کارت ۹
پرسش
What four features should a description of a quantitative distribution address?
پاسخ
Shape, center, variability, and unusual features such as gaps or outliers.
کارت ۱۰
پرسش
Which measure of center is usually better for a strongly right-skewed distribution?
پاسخ
The median, because it is resistant to extreme high values.
کارت ۱۱
پرسش
The values are 3, 5, 5, and 11. What is the mean?
پاسخ
- The sum is 24, divided by 4 observations.
کارت ۱۲
پرسش
The ordered values are 2, 4, 7, 9, 12, and 20. What is the median?
پاسخ
8, the average of the two middle values 7 and 9.
کارت ۱۳
پرسش
How is the interquartile range calculated?
پاسخ
IQR = Q3 − Q1. It measures the spread of the middle 50% of the data.
کارت ۱۴
پرسش
What does a small standard deviation say about a data set?
پاسخ
Values typically lie close to the mean.
کارت ۱۵
پرسش
Which common summaries are resistant to extreme values?
پاسخ
The median and IQR are resistant; the mean and standard deviation are not.
کارت ۱۶
پرسش
In a modified boxplot, where do the whiskers end?
پاسخ
At the smallest and largest observed values within the 1.5 × IQR fences; values beyond the fences are plotted separately as potential outliers.
کارت ۱۷
پرسش
What are the 1.5 × IQR outlier fences?
پاسخ
Lower fence = Q1 − 1.5(IQR); upper fence = Q3 + 1.5(IQR). Values beyond them are flagged as potential outliers.
کارت ۱۸
پرسش
How should two quantitative distributions be compared?
پاسخ
Compare shape, center, variability, and unusual features in context, using the same measure or display basis.
کارت ۱۹
پرسش
What does a z-score of −1.8 mean?
پاسخ
The value is 1.8 standard deviations below the mean.
کارت ۲۰
پرسش
Every observation is converted from meters to centimeters by multiplying by 100. What happens to the mean and standard deviation?
پاسخ
Both are multiplied by 100.
کارت ۲۱
پرسش
What should an investigative question identify so the conclusion has a clear scope?
پاسخ
The variable or parameter of interest and the population to which the conclusion may apply.
کارت ۲۲
پرسش
What is a census?
پاسخ
A study that collects data from every member of the population.
کارت ۲۳
پرسش
What makes a study an experiment?
پاسخ
Researchers deliberately assign treatments to experimental units.
کارت ۲۴
پرسش
How do prospective and retrospective observational studies differ?
پاسخ
A prospective study follows units forward and gathers future data; a retrospective study uses data from the past.
کارت ۲۵
پرسش
What is a confounding variable in an observational study?
پاسخ
A variable associated with both the explanatory and response variables that offers an alternative explanation for their relationship.
کارت ۲۶
پرسش
What study feature supports generalizing results to a population?
پاسخ
Random selection from that population.
کارت ۲۷
پرسش
What makes a study observational?
پاسخ
Researchers observe variables without assigning treatments.
کارت ۲۸
پرسش
What study feature supports a cause-and-effect conclusion?
پاسخ
Random assignment of treatments in a well-designed experiment.
کارت ۲۹
پرسش
What defines a simple random sample of size n?
پاسخ
Every possible sample of size n has the same chance of selection.
کارت ۳۰
پرسش
What changes when sampling is done with replacement?
پاسخ
A selected unit returns to the population and can be selected again.
کارت ۳۱
پرسش
Why can a convenience sample be biased?
پاسخ
Easy-to-reach units may differ systematically from the target population.
کارت ۳۲
پرسش
Why should an experiment compare at least two treatment groups?
پاسخ
The comparison provides a baseline for judging whether responses differ by treatment.
کارت ۳۳
پرسش
A school samples 20 students at random from each grade. Which sampling method is this?
پاسخ
Stratified random sampling, with grade as the stratum.
کارت ۳۴
پرسش
What is the purpose of random assignment?
پاسخ
It tends to balance lurking variables across treatment groups, supporting causal inference.
کارت ۳۵
پرسش
Why can a voluntary-response sample be biased?
پاسخ
People with strong opinions are often more likely to participate.
کارت ۳۶
پرسش
What does replication mean in an experiment?
پاسخ
Assigning more than one experimental unit to each treatment so treatment differences can be separated from individual variability.
کارت ۳۷
پرسش
A city randomly selects 8 apartment buildings and surveys every household in those buildings. Which method is this?
پاسخ
Cluster random sampling.
کارت ۳۸
پرسش
What does direct control do in an experiment?
پاسخ
It holds potential extraneous sources of variation constant across experimental units.
کارت ۳۹
پرسش
What is undercoverage?
پاسخ
Some groups in the target population are left out of, or poorly represented in, the sampling frame.
کارت ۴۰
پرسش
What is the role of a control group?
پاسخ
It supplies a comparison condition for evaluating the treatment of interest.
کارت ۴۱
پرسش
After a random start, a quality inspector checks every 40th item. Which sampling method is this?
پاسخ
Systematic random sampling.
کارت ۴۲
پرسش
Why might an experiment use a placebo?
پاسخ
To separate a treatment's effect from responses caused by expecting treatment.
کارت ۴۳
پرسش
What is nonresponse bias?
پاسخ
Selected individuals who do not respond differ in a relevant way from those who do.
کارت ۴۴
پرسش
What is single blinding designed to reduce?
پاسخ
Bias caused when participants or evaluators know which treatment was received, depending on who is blinded.
کارت ۴۵
پرسش
Why use a randomized block design?
پاسخ
To group units that are similar on an important source of variation, then compare treatments within each block.
کارت ۴۶
پرسش
What defines a matched-pairs design?
پاسخ
Two treatments are compared using paired similar units or by giving both treatments to each unit in randomized order.
کارت ۴۷
پرسش
A survey asks, “Don't you agree the new schedule is unfair?” What problem does this create?
پاسخ
Response bias from leading wording.
کارت ۴۸
پرسش
What usually makes an experiment double-blind?
پاسخ
Neither the participants nor the people evaluating responses know treatment assignments while outcomes are measured.
کارت ۴۹
پرسش
A researcher randomly assigns 80 volunteers to two diets and compares blood-pressure change. What conclusion can random assignment support?
پاسخ
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.
کارت ۵۰
پرسش
A researcher records coffee intake and sleep duration without assigning either. Can the study establish that coffee causes less sleep?
پاسخ
No. It is observational, so confounding can provide alternative explanations.
کارت ۵۱
پرسش
What is the difference between a population and a sample?
پاسخ
The population is the full group of interest; a sample is the subset actually observed.
کارت ۵۲
پرسش
Which graph is appropriate for the distribution of one quantitative variable measured on 600 people?
پاسخ
A histogram is appropriate; it groups the many numerical values into intervals.
کارت ۵۳
پرسش
In a strongly right-skewed distribution, how do the mean and median usually compare?
پاسخ
The mean is usually larger because high values pull it to the right.
کارت ۵۴
پرسش
Every score increases by 7 points. What happens to the mean and standard deviation?
پاسخ
The mean increases by 7; the standard deviation stays unchanged.
کارت ۵۵
پرسش
What does it mean that a score is at the 80th percentile?
پاسخ
About 80% of scores are at or below it.
کارت ۵۶
پرسش
Why should gaps and clusters be mentioned when describing a distribution?
پاسخ
They may reveal distinct subgroups, collection effects, or other structure that center and spread alone hide.
کارت ۵۷
پرسش
What is the minimum ethical safeguard when collecting identifiable human data?
پاسخ
Obtain informed consent when required and protect participants' privacy and confidentiality.
کارت ۵۸
پرسش
Every measurement is multiplied by −2. What happens to the mean and standard deviation?
پاسخ
The mean is multiplied by −2; the standard deviation is multiplied by 2.
کارت ۵۹
پرسش
A study uses random sampling but no assigned treatment. What can it support?
پاسخ
Population generalization, but not a cause-and-effect conclusion.
کارت ۶۰
پرسش
A report calls any unmeasured variable a confounder. What is the correction?
پاسخ
A confounder must be related to both the explanatory and response variables and create an alternative explanation.
کارت ۶۱
پرسش
What does a two-way table summarize?
پاسخ
Counts or relative frequencies for combinations of two categorical variables.
کارت ۶۲
پرسش
What is a joint relative frequency?
پاسخ
A cell count divided by the grand total, representing one combination of categories.
کارت ۶۳
پرسش
What is a marginal relative frequency?
پاسخ
A row or column total divided by the grand total.
کارت ۶۴
پرسش
How is a conditional relative frequency calculated within one row?
پاسخ
Divide each cell in that row by the row total.
کارت ۶۵
پرسش
What pattern suggests association between two categorical variables?
پاسخ
The conditional distribution of one variable changes across categories of the other.
کارت ۶۶
پرسش
Why are segmented bar charts useful for two categorical variables?
پاسخ
They place conditional distributions on the same 100% scale, making category patterns easy to compare.
کارت ۶۷
پرسش
How do an outcome and an event differ?
پاسخ
An outcome is one result of a trial; an event is a set of one or more outcomes.
کارت ۶۸
پرسش
What must a valid probability simulation specify?
پاسخ
A chance mechanism whose outcomes match the event probabilities, one trial definition, the statistic recorded, and many repetitions.
کارت ۶۹
پرسش
What does the law of large numbers predict?
پاسخ
As independent trials accumulate, an event's long-run relative frequency tends to approach its probability.
کارت ۷۰
پرسش
What two requirements must probabilities in a sample space satisfy?
پاسخ
Each probability is between 0 and 1, and the probabilities of all nonoverlapping outcomes sum to 1.
کارت ۷۱
پرسش
What is the complement rule?
پاسخ
P(Aᶜ) = 1 − P(A). It is often useful for “at least one” events.
کارت ۷۲
پرسش
How can you verify that events A and B are mutually exclusive?
پاسخ
Their intersection is impossible, so P(A ∩ B) = 0.
کارت ۷۳
پرسش
What is the formula for P(A | B), when P(B) > 0?
پاسخ
P(A | B) = P(A ∩ B) / P(B). The restricted sample space is B.
کارت ۷۴
پرسش
What is the general multiplication rule for two events?
پاسخ
P(A ∩ B) = P(A)P(B | A), or equivalently P(B)P(A | B).
کارت ۷۵
پرسش
What does it mean for events A and B to be independent?
پاسخ
Knowing that one occurred does not change the probability of the other.
کارت ۷۶
پرسش
What is the general addition rule?
پاسخ
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
کارت ۷۷
پرسش
Why are two mutually exclusive events with positive probabilities not independent?
پاسخ
If one occurs, the other cannot occur, so its conditional probability drops to 0.
کارت ۷۸
پرسش
What is a random variable?
پاسخ
A numerical value determined by the outcome of a random process.
کارت ۷۹
پرسش
What makes a table a valid discrete probability distribution?
پاسخ
It lists every possible value with probabilities from 0 to 1 that sum to 1.
کارت ۸۰
پرسش
What does a cumulative distribution value F(x) represent?
پاسخ
P(X ≤ x), the probability that the random variable is at most x.
کارت ۸۱
پرسش
How is the expected value of a discrete random variable calculated?
پاسخ
Multiply each possible value by its probability and add: E(X) = ΣxP(X = x).
کارت ۸۲
پرسش
What does the standard deviation of a random variable measure?
پاسخ
The typical distance of long-run outcomes from the random variable's mean.
کارت ۸۳
پرسش
How is the standard deviation of a discrete random variable calculated?
پاسخ
σₓ = √[Σ(x − μₓ)²P(X = x)]. The quantity inside the square root is Var(X).
کارت ۸۴
پرسش
A game has E(X) = −$0.40 per play. What does this mean?
پاسخ
Over many plays, the player's average net result approaches a loss of 40 cents per play; it does not predict every play.
کارت ۸۵
پرسش
What conditions define a binomial random variable?
پاسخ
A fixed number of independent trials, two outcomes per trial, constant success probability, and X counts successes.
کارت ۸۶
پرسش
For X ~ Binomial(n, p), what are the mean and standard deviation?
پاسخ
Mean = np; standard deviation = √[np(1 − p)].
کارت ۸۷
پرسش
For X ~ Binomial(n, p), what is P(X = x)?
پاسخ
Choose x success positions, then multiply: C(n, x)pˣ(1 − p)ⁿ⁻ˣ.
کارت ۸۸
پرسش
How can P(X ≥ 1) be found efficiently for a binomial variable?
پاسخ
Use the complement: P(X ≥ 1) = 1 − P(X = 0).
کارت ۸۹
پرسش
What should one simulated trial represent when estimating P(X ≥ 4) for X ~ Binomial(10, 0.3)?
پاسخ
Ten independent success/failure observations with success probability 0.3, followed by recording whether at least four successes occurred.
کارت ۹۰
پرسش
What features characterize a normal distribution?
پاسخ
It is continuous, symmetric, unimodal, and bell-shaped.
کارت ۹۱
پرسش
Which parameters determine a normal distribution?
پاسخ
Its mean μ sets the center, and its standard deviation σ sets the spread.
کارت ۹۲
پرسش
What is the standard normal distribution?
پاسخ
The normal distribution with mean 0 and standard deviation 1.
کارت ۹۳
پرسش
What is the 68–95–99.7 rule?
پاسخ
For an approximately normal distribution, about 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations of the mean.
کارت ۹۴
پرسش
What does an area under a normal curve represent?
پاسخ
The probability or population proportion within the corresponding interval.
کارت ۹۵
پرسش
How do you find the value cutting off the lowest 10% of a normal distribution?
پاسخ
Find the z-score with cumulative area 0.10, then convert with x = μ + zσ.
کارت ۹۶
پرسش
A normal variable has μ = 50 and σ = 8. What z-score corresponds to x = 62?
پاسخ
1.5, because z = (62 − 50) / 8.
کارت ۹۷
پرسش
Two exam scores come from different normal distributions. What makes their percentiles comparable?
پاسخ
Standardize each score with its own distribution's mean and standard deviation, then compare z-scores or cumulative areas.
کارت ۹۸
پرسش
What is a sampling distribution of a statistic?
پاسخ
The distribution of that statistic over all possible random samples of a fixed size from a population.
کارت ۹۹
پرسش
How can a sampling distribution be approximated by simulation?
پاسخ
Repeatedly take random samples of the same size, calculate the statistic each time, and graph the resulting values.
کارت ۱۰۰
پرسش
What is a randomization distribution?
پاسخ
A simulated distribution of a statistic produced by repeatedly reallocating responses or labels as specified by a null model.
کارت ۱۰۱
پرسش
What does the central limit theorem say about sample means?
پاسخ
For random samples, the sampling distribution of the sample mean becomes approximately normal as sample size grows, even when the population is not normal.
کارت ۱۰۲
پرسش
How does increasing sample size affect the normal approximation in the central limit theorem?
پاسخ
It generally improves the approximation, especially for skewed or irregular populations.
کارت ۱۰۳
پرسش
A segmented bar chart shows nearly identical category proportions for every group. What does that suggest?
پاسخ
Little or no association between the two categorical variables.
کارت ۱۰۴
پرسش
In a survey, 30 of 120 students both bike to school and arrive before 8:00. What is the joint relative frequency?
پاسخ
0.25, because 30 / 120 = 0.25.
کارت ۱۰۵
پرسش
Why can P(A | B) differ from P(B | A)?
پاسخ
They use different restricted sample spaces and usually have different denominators.
کارت ۱۰۶
پرسش
If P(A) = 0.4 and P(A | B) = 0.4 with P(B) > 0, what does this indicate?
پاسخ
A and B are independent because learning B does not change the probability of A.
کارت ۱۰۷
پرسش
If independent events have probabilities 0.6 and 0.5, what is the probability that both occur?
پاسخ
0.30, using P(A ∩ B) = P(A)P(B).
کارت ۱۰۸
پرسش
A prize is $0 with probability 0.7 and $10 with probability 0.3. What is the expected prize?
پاسخ
$3, because 0(0.7) + 10(0.3) = 3.
کارت ۱۰۹
پرسش
A machine produces defective items independently with probability 0.02. What distribution models the number of defectives in 50 items?
پاسخ
Binomial with n = 50 and p = 0.02.
کارت ۱۱۰
پرسش
Heights are approximately normal with μ = 170 cm and σ = 6 cm. About what percent lie from 158 to 182 cm?
پاسخ
About 95%, because the interval is μ ± 2σ.
کارت ۱۱۱
پرسش
What makes an estimator unbiased?
پاسخ
Its sampling distribution is centered at the population parameter it estimates.
کارت ۱۱۲
پرسش
For random samples of size n, what is the mean of the sampling distribution of p̂?
پاسخ
μₚ̂ = p, where p is the population proportion.
کارت ۱۱۳
پرسش
Which procedure estimates one population proportion from a random sample?
پاسخ
A one-sample z-interval for a population proportion.
کارت ۱۱۴
پرسش
How should a confidence interval for a population proportion be interpreted?
پاسخ
We are confident at the stated level that the interval captures the true population proportion, in context.
کارت ۱۱۵
پرسش
What hypotheses test whether a population proportion differs from 0.40?
پاسخ
H₀: p = 0.40 versus Hₐ: p ≠ 0.40.
کارت ۱۱۶
پرسش
What is a p-value?
پاسخ
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.
کارت ۱۱۷
پرسش
What is the hypothesis-test decision rule using significance level α?
پاسخ
Reject H₀ when the p-value ≤ α; otherwise fail to reject H₀.
کارت ۱۱۸
پرسش
What is a Type I error?
پاسخ
Rejecting H₀ when H₀ is actually true.
کارت ۱۱۹
پرسش
What is the mean of p̂₁ − p̂₂ for independent random samples?
پاسخ
p₁ − p₂.
کارت ۱۲۰
پرسش
Which procedure estimates p₁ − p₂ from two independent samples or randomized groups?
پاسخ
A two-sample z-interval for a difference between population proportions.
کارت ۱۲۱
پرسش
How should a confidence interval for p₁ − p₂ be interpreted?
پاسخ
We are confident at the stated level that the interval captures the true difference p₁ − p₂, in context.
کارت ۱۲۲
پرسش
What null hypothesis is standard when testing whether two population proportions differ?
پاسخ
H₀: p₁ − p₂ = 0, equivalently p₁ = p₂.
کارت ۱۲۳
پرسش
A two-proportion test gives p-value 0.018 at α = 0.05. What decision follows?
پاسخ
Reject H₀ because 0.018 < 0.05.
کارت ۱۲۴
پرسش
When is a chi-square test for independence appropriate?
پاسخ
When one random sample provides two categorical variables and the question asks whether they are associated in one population.
کارت ۱۲۵
پرسش
How should a chi-square test p-value be interpreted?
پاسخ
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.
۲۵۰ کارت
AP Statistics Flashcards: Complete 5-Unit Course Review
این دسته را رایگان مطالعه کنیدNibomo باز میشود تا بتوانید مطالعه را شروع کنید.
کارت ۱۲۶
پرسش
How do bias and variability differ for an estimator?
پاسخ
Bias concerns where the sampling distribution is centered; variability concerns how spread out it is.
کارت ۱۲۷
پرسش
What is the standard deviation of p̂ when observations are independent?
پاسخ
σₚ̂ = √[p(1 − p) / n].
کارت ۱۲۸
پرسش
What is the one-proportion z-interval formula?
پاسخ
p̂ ± z*√[p̂(1 − p̂) / n].
کارت ۱۲۹
پرسش
What does a 95% confidence level describe?
پاسخ
In repeated random sampling with the same method, about 95% of the resulting intervals would capture the true parameter.
کارت ۱۳۰
پرسش
Which method tests a claim about one population proportion when its conditions hold?
پاسخ
A one-sample z-test for a population proportion.
کارت ۱۳۱
پرسش
How does the alternative hypothesis determine a p-value's tail area?
پاسخ
A greater-than alternative uses the upper tail, a less-than alternative uses the lower tail, and a not-equal alternative uses both tails.
کارت ۱۳۲
پرسش
What wording should follow a rejected null hypothesis?
پاسخ
There is convincing statistical evidence for the alternative claim about the population parameter, stated in context.
کارت ۱۳۳
پرسش
What is a Type II error?
پاسخ
Failing to reject H₀ when Hₐ is actually true.
کارت ۱۳۴
پرسش
What is the standard deviation of p̂₁ − p̂₂ for independent samples?
پاسخ
√[p₁(1 − p₁)/n₁ + p₂(1 − p₂)/n₂].
کارت ۱۳۵
پرسش
What standard error is used in a confidence interval for p₁ − p₂?
پاسخ
√[p̂₁(1 − p̂₁)/n₁ + p̂₂(1 − p̂₂)/n₂]; the sample proportions are not pooled.
کارت ۱۳۶
پرسش
A confidence interval for p₁ − p₂ contains 0. What does that imply?
پاسخ
The interval does not provide convincing evidence of a difference between the population proportions at the corresponding two-sided significance level.
کارت ۱۳۷
پرسش
Why is a pooled proportion used in a two-proportion z-test with H₀: p₁ = p₂?
پاسخ
The null model assumes both samples share one common population proportion, estimated by combining successes and observations.
کارت ۱۳۸
پرسش
How should a p-value for a two-proportion test be stated?
پاسخ
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.
کارت ۱۳۹
پرسش
When is a chi-square test for homogeneity appropriate?
پاسخ
When independent samples or randomized groups are compared on the distribution of one categorical response variable.
کارت ۱۴۰
پرسش
What is the chi-square test statistic formula?
پاسخ
χ² = Σ[(observed − expected)² / expected], summed over all cells.
کارت ۱۴۱
پرسش
What usually happens to an estimator's sampling variability as sample size increases?
پاسخ
It decreases; estimates from larger random samples tend to cluster more tightly around the parameter.
کارت ۱۴۲
پرسش
When is the sampling distribution of p̂ approximately normal?
پاسخ
When the expected counts np and n(1 − p) are both at least 10.
کارت ۱۴۳
پرسش
What conditions justify a one-proportion z-interval?
پاسخ
Random data; independence, checked with n ≤ 10% of the population when sampling without replacement; and at least 10 observed successes and 10 observed failures.
کارت ۱۴۴
پرسش
A 95% confidence interval for p is (0.52, 0.61). What does it say about the claim p = 0.50?
پاسخ
The interval excludes 0.50, so the data provide evidence against p = 0.50 in a two-sided test at α = 0.05.
کارت ۱۴۵
پرسش
What is the one-proportion z-test statistic?
پاسخ
z = (p̂ − p₀) / √[p₀(1 − p₀)/n], using the null proportion p₀ in the standard error.
کارت ۱۴۶
پرسش
How is a simulation-based p-value estimated?
پاسخ
Find the proportion of simulated null statistics at least as extreme as the observed statistic in the direction of Hₐ.
کارت ۱۴۷
پرسش
What does “fail to reject H₀” mean?
پاسخ
The data do not provide convincing evidence for Hₐ; it does not prove H₀ true.
کارت ۱۴۸
پرسش
With sample size and effect fixed, what often happens when α is lowered?
پاسخ
The chance of a Type I error decreases, while the chance of a Type II error increases.
کارت ۱۴۹
پرسش
What conditions support the usual model for p̂₁ − p̂₂?
پاسخ
Independent random samples or randomized groups, independence within each group, and large enough expected success and failure counts for normal approximation.
کارت ۱۵۰
پرسش
What conditions justify a two-proportion z-interval?
پاسخ
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.
کارت ۱۵۱
پرسش
How does increasing both sample sizes affect a confidence interval for p₁ − p₂?
پاسخ
It reduces the standard error and usually narrows the interval when other factors stay the same.
کارت ۱۵۲
پرسش
What standard error is used in the two-proportion z-test?
پاسخ
√[p̂c(1 − p̂c)(1/n₁ + 1/n₂)], where p̂c is the pooled sample proportion.
کارت ۱۵۳
پرسش
A randomized experiment uses volunteers assigned to two treatments. A significant two-proportion test supports what scope?
پاسخ
A cause-and-effect conclusion for people similar to the volunteers, not automatic generalization to a broader population.
کارت ۱۵۴
پرسش
How is an expected count computed in a two-way table under independence?
پاسخ
Expected count = (row total × column total) / grand total.
کارت ۱۵۵
پرسش
What conditions justify a chi-square test for a two-way table?
پاسخ
Random data; independent observations, including the 10% check when sampling without replacement; and every expected cell count greater than 5.
کارت ۱۵۶
پرسش
A sampling distribution is centered away from the true parameter. What problem does this reveal?
پاسخ
Bias in the estimator.
کارت ۱۵۷
پرسش
If p = 0.30 and n = 100, what does μₚ̂ = 0.30 mean?
پاسخ
Across many random samples of 100, the average sample proportion would be 0.30.
کارت ۱۵۸
پرسش
For a planned proportion interval with margin of error m, what conservative p-value is used when no prior estimate exists?
پاسخ
Use p* = 0.50 in n ≥ (z*/m)²p*(1 − p*) because it gives the largest required sample size.
کارت ۱۵۹
پرسش
What two changes widen a confidence interval for a proportion?
پاسخ
Using a higher confidence level or a smaller sample size.
کارت ۱۶۰
پرسش
Which counts check normality for a one-proportion z-test?
پاسخ
Use the null model: np₀ ≥ 10 and n(1 − p₀) ≥ 10.
کارت ۱۶۱
پرسش
What is wrong with saying “the p-value is the probability that H₀ is true”?
پاسخ
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.
کارت ۱۶۲
پرسش
What does “statistically significant at α = 0.01” mean?
پاسخ
The p-value is at most 0.01, so H₀ is rejected at that significance level.
کارت ۱۶۳
پرسش
What is the power of a hypothesis test?
پاسخ
The probability that the test rejects H₀ when a particular alternative is true.
کارت ۱۶۴
پرسش
If p₁ = p₂, where is the sampling distribution of p̂₁ − p̂₂ centered?
پاسخ
At 0, because its mean is p₁ − p₂.
کارت ۱۶۵
پرسش
Why must the order p̂₁ − p̂₂ stay consistent throughout an interval?
پاسخ
Changing the order reverses the sign and changes the contextual interpretation of every endpoint.
کارت ۱۶۶
پرسش
A 95% interval for p₁ − p₂ is (0.04, 0.15). What conclusion is supported?
پاسخ
p₁ is plausibly 0.04 to 0.15 higher than p₂; the interval supports a positive difference.
کارت ۱۶۷
پرسش
Which success-failure counts are checked for a two-proportion z-test?
پاسخ
Expected counts based on the pooled null proportion: n₁p̂c, n₁(1 − p̂c), n₂p̂c, and n₂(1 − p̂c), each at least 10.
کارت ۱۶۸
پرسش
A two-proportion test with Hₐ: p₁ ≠ p₂ fails to reject H₀. What conclusion is valid?
پاسخ
There is not convincing evidence that the two population proportions differ.
کارت ۱۶۹
پرسش
What are the degrees of freedom for a chi-square test on an r × c table?
پاسخ
(r − 1)(c − 1).
کارت ۱۷۰
پرسش
A chi-square test for independence has a small p-value. What conclusion is appropriate?
پاسخ
There is convincing evidence of an association between the two categorical variables in the population, stated in context.
کارت ۱۷۱
پرسش
What is the mean of the sampling distribution of x̄ for random samples from a population with mean μ?
پاسخ
μₓ̄ = μ.
کارت ۱۷۲
پرسش
Which procedure estimates one population mean when the population standard deviation is unknown?
پاسخ
A one-sample t-interval for a population mean.
کارت ۱۷۳
پرسش
How should a confidence interval for a population mean be interpreted?
پاسخ
We are confident at the stated level that the interval captures the true population mean, in context.
کارت ۱۷۴
پرسش
What hypotheses test whether a population mean exceeds 12?
پاسخ
H₀: μ = 12 versus Hₐ: μ > 12.
کارت ۱۷۵
پرسش
A one-sample t-test gives p-value 0.08 at α = 0.05. What decision follows?
پاسخ
Fail to reject H₀ because 0.08 > 0.05.
کارت ۱۷۶
پرسش
What is the mean of x̄₁ − x̄₂ for independent random samples?
پاسخ
μ₁ − μ₂.
کارت ۱۷۷
پرسش
Which procedure estimates μ₁ − μ₂ from two independent samples?
پاسخ
A two-sample t-interval for a difference between population means.
کارت ۱۷۸
پرسش
How should a confidence interval for μ₁ − μ₂ be interpreted?
پاسخ
We are confident at the stated level that the interval captures the true difference μ₁ − μ₂, in context.
کارت ۱۷۹
پرسش
What null hypothesis is standard when testing whether two population means differ?
پاسخ
H₀: μ₁ − μ₂ = 0, equivalently μ₁ = μ₂.
کارت ۱۸۰
پرسش
A two-sample t-test gives p-value 0.004 at α = 0.01. What decision follows?
پاسخ
Reject H₀ because 0.004 < 0.01.
کارت ۱۸۱
پرسش
What is the standard deviation of x̄ when observations are independent?
پاسخ
σₓ̄ = σ / √n.
کارت ۱۸۲
پرسش
What is the one-sample t-interval formula for μ?
پاسخ
x̄ ± t* × s/√n, with t* based on n − 1 degrees of freedom.
کارت ۱۸۳
پرسش
What does a 90% confidence level mean for a mean interval procedure?
پاسخ
Across many random samples using the same procedure, about 90% of the intervals would capture the true population mean.
کارت ۱۸۴
پرسش
Which procedure tests a claim about one population mean when σ is unknown?
پاسخ
A one-sample t-test for a population mean.
کارت ۱۸۵
پرسش
How should a one-mean test p-value be interpreted?
پاسخ
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.
کارت ۱۸۶
پرسش
What is the standard deviation of x̄₁ − x̄₂ for independent samples?
پاسخ
√(σ₁²/n₁ + σ₂²/n₂).
کارت ۱۸۷
پرسش
What standard error is used in a two-sample t-interval for μ₁ − μ₂?
پاسخ
√(s₁²/n₁ + s₂²/n₂).
کارت ۱۸۸
پرسش
A confidence interval for μ₁ − μ₂ contains 0. What does that imply?
پاسخ
The interval does not provide convincing evidence of a difference between the population means at the corresponding two-sided significance level.
کارت ۱۸۹
پرسش
What is the two-sample t-statistic for testing H₀: μ₁ − μ₂ = 0?
پاسخ
t = [(x̄₁ − x̄₂) − 0] / √(s₁²/n₁ + s₂²/n₂).
کارت ۱۹۰
پرسش
How should a two-mean test p-value be interpreted?
پاسخ
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.
کارت ۱۹۱
پرسش
When is the sampling distribution of x̄ approximately normal?
پاسخ
When the population is approximately normal or the random sample is large enough for the central limit theorem to apply.
کارت ۱۹۲
پرسش
What conditions justify a one-sample t-interval?
پاسخ
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.
کارت ۱۹۳
پرسش
How does increasing sample size affect a confidence interval for μ?
پاسخ
It lowers the standard error and usually narrows the interval when confidence level and variability stay comparable.
کارت ۱۹۴
پرسش
What is the one-sample t-test statistic?
پاسخ
t = (x̄ − μ₀) / (s/√n), with n − 1 degrees of freedom.
کارت ۱۹۵
پرسش
A t-test fails to reject H₀. What should the conclusion avoid?
پاسخ
Avoid saying H₀ is true; say the data do not provide convincing evidence for Hₐ.
کارت ۱۹۶
پرسش
When is x̄₁ − x̄₂ approximately normal?
پاسخ
When both populations are approximately normal or both independent random samples are large enough for normal approximations.
کارت ۱۹۷
پرسش
What conditions justify a two-sample t-interval?
پاسخ
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.
کارت ۱۹۸
پرسش
A 95% interval for μ₁ − μ₂ is (−7.2, −1.4). What does it support?
پاسخ
μ₁ is plausibly 1.4 to 7.2 units lower than μ₂; the interval supports a negative difference.
کارت ۱۹۹
پرسش
What sample-shape condition is checked for a two-sample t-test with small samples?
پاسخ
Both sample distributions should be free of strong skewness and outliers unless both populations are known to be approximately normal.
کارت ۲۰۰
پرسش
A randomized experiment finds a significant difference in mean response. What can random assignment support?
پاسخ
A cause-and-effect conclusion for units like those studied, assuming the experiment was well designed.
کارت ۲۰۱
پرسش
A population has μ = 40. What does μₓ̄ = 40 mean for samples of size 25?
پاسخ
Across all random samples of 25, the average sample mean is 40.
کارت ۲۰۲
پرسش
How is a matched-pairs confidence interval analyzed?
پاسخ
Compute one difference for each pair, then use a one-sample t-interval on the population mean difference.
کارت ۲۰۳
پرسش
A 95% confidence interval for μ is (18.2, 21.7). What does it say about μ = 22?
پاسخ
The interval excludes 22, providing evidence against μ = 22 in a two-sided test at α = 0.05.
کارت ۲۰۴
پرسش
Which observations enter a matched-pairs t-test?
پاسخ
The within-pair differences, not the two original columns treated as independent samples.
کارت ۲۰۵
پرسش
A test reports p-value 0.032. At which common levels is it significant: 0.05 or 0.01?
پاسخ
Significant at 0.05, but not at 0.01.
کارت ۲۰۶
پرسش
If μ₁ − μ₂ = 5, where is the sampling distribution of x̄₁ − x̄₂ centered?
پاسخ
At 5.
کارت ۲۰۷
پرسش
Does the standard AP two-sample t procedure require equal population variances?
پاسخ
No. It uses separate sample variances in the standard error rather than pooling them.
کارت ۲۰۸
پرسش
What two changes usually widen a confidence interval for μ₁ − μ₂?
پاسخ
Higher confidence or smaller sample sizes.
کارت ۲۰۹
پرسش
Why must the order x̄₁ − x̄₂ match the order μ₁ − μ₂ in the hypotheses?
پاسخ
Reversing the order reverses the sign and changes the direction of the claim.
کارت ۲۱۰
پرسش
A two-sample test with Hₐ: μ₁ > μ₂ fails to reject H₀. What conclusion is valid?
پاسخ
There is not convincing evidence that μ₁ exceeds μ₂.
کارت ۲۱۱
پرسش
A population has σ = 18 and random samples have n = 36. What is σₓ̄?
پاسخ
3, because 18/√36 = 3.
کارت ۲۱۲
پرسش
Why is a t distribution used for inference about a mean when σ is unknown?
پاسخ
Replacing σ with the sample standard deviation s adds uncertainty, which the heavier-tailed t distribution accounts for.
کارت ۲۱۳
پرسش
What conditions justify a one-sample t-test?
پاسخ
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.
کارت ۲۱۴
پرسش
What distinguishes a two-sample means procedure from a matched-pairs procedure?
پاسخ
Two-sample procedures use independent groups; matched-pairs procedures analyze linked observations through their differences.
کارت ۲۱۵
پرسش
How are degrees of freedom handled for a two-sample t procedure?
پاسخ
Technology usually uses an approximation based on both sample variances and sizes; a conservative fallback uses the smaller of n₁ − 1 and n₂ − 1.
کارت ۲۱۶
پرسش
What type of variables belong on a scatterplot?
پاسخ
Two quantitative variables measured on the same observational units.
کارت ۲۱۷
پرسش
What does the correlation coefficient r describe?
پاسخ
The direction and strength of a linear relationship between two quantitative variables.
کارت ۲۱۸
پرسش
What does ŷ = a + bx represent?
پاسخ
A linear regression model predicting response y from explanatory variable x.
کارت ۲۱۹
پرسش
What is a residual?
پاسخ
Observed response minus predicted response: residual = y − ŷ.
کارت ۲۲۰
پرسش
What makes a regression line the least-squares line?
پاسخ
It minimizes the sum of squared residuals.
کارت ۲۲۱
پرسش
What four features should a scatterplot description address?
پاسخ
Direction, form, strength, and unusual features such as outliers or clusters.
کارت ۲۲۲
پرسش
What values can r take?
پاسخ
Any value from −1 to 1, inclusive.
کارت ۲۲۳
پرسش
How is the slope b interpreted in context?
پاسخ
For each one-unit increase in x, the predicted value of y changes by b units on average.
کارت ۲۲۴
پرسش
What does a positive residual mean?
پاسخ
The observed response is above the model's predicted response.
کارت ۲۲۵
پرسش
What is the least-squares slope formula?
پاسخ
b = r(sᵧ/sₓ).
کارت ۲۲۶
پرسش
A scatterplot trends downward from left to right. What direction is the association?
پاسخ
Negative: larger x-values tend to occur with smaller y-values.
کارت ۲۲۷
پرسش
Why can r be near 0 even when two variables are strongly related?
پاسخ
Correlation measures only linear association, so a strong curved relationship can have r near 0.
کارت ۲۲۸
پرسش
How is the intercept a interpreted in context?
پاسخ
It is the predicted response when x = 0, provided x = 0 is meaningful and within the data's scope.
کارت ۲۲۹
پرسش
A model predicts 18, and the observed response is 21. What is the residual?
پاسخ
3, because 21 − 18 = 3.
کارت ۲۳۰
پرسش
How is the least-squares intercept found from the slope?
پاسخ
a = ȳ − bx̄.
کارت ۲۳۱
پرسش
What makes a linear association look strong?
پاسخ
The points lie close to a straight-line pattern, regardless of whether the slope is steep or shallow.
کارت ۲۳۲
پرسش
Does r have measurement units?
پاسخ
No. Correlation is unitless because it is based on standardized values.
کارت ۲۳۳
پرسش
For ŷ = 12 + 2.5x, what is predicted when x = 4?
پاسخ
22, because 12 + 2.5(4) = 22.
کارت ۲۳۴
پرسش
What residual-plot pattern supports using a linear model?
پاسخ
Random scatter around zero with no clear curve, trend, or changing spread.
کارت ۲۳۵
پرسش
What does r² measure in simple linear regression?
پاسخ
The proportion of variation in the response variable explained by its linear relationship with the explanatory variable.
کارت ۲۳۶
پرسش
A scatterplot shows a strong association. Does that establish causation?
پاسخ
No. A scatterplot alone cannot rule out confounding or other explanations.
کارت ۲۳۷
پرسش
Why should unusual points be checked before interpreting r?
پاسخ
Correlation is not resistant; an outlier or influential point can change r substantially.
کارت ۲۳۸
پرسش
Why is extrapolation risky?
پاسخ
The relationship observed over the data range may not continue beyond that range.
کارت ۲۳۹
پرسش
A point lies below the regression line. What sign is its residual?
پاسخ
Negative, because observed y is less than predicted ŷ.
کارت ۲۴۰
پرسش
Which point always lies on a least-squares regression line with an intercept?
پاسخ
The point (x̄, ȳ).
کارت ۲۴۱
پرسش
Which variable goes on each axis of a scatterplot used for prediction?
پاسخ
The explanatory variable goes on the horizontal x-axis; the response variable goes on the vertical y-axis.
کارت ۲۴۲
پرسش
What happens to r if the roles of x and y are swapped?
پاسخ
Nothing. Correlation is symmetric.
کارت ۲۴۳
پرسش
What is interpolation?
پاسخ
Predicting a response for an x-value within the range of observed explanatory values.
کارت ۲۴۴
پرسش
A residual plot has a clear U-shape. What is the correction?
پاسخ
Do not treat the linear model as adequate; the curved pattern shows systematic structure remains.
کارت ۲۴۵
پرسش
A regression has r² = 0.64. What does this mean?
پاسخ
About 64% of the variation in the response is explained by its linear relationship with the explanatory variable.
کارت ۲۴۶
پرسش
What is an outlier in a scatterplot?
پاسخ
A point that falls away from the overall pattern of the other points.
کارت ۲۴۷
پرسش
What happens to r when x is converted from centimeters to meters?
پاسخ
It stays the same because multiplying by a positive constant does not change standardized linear association.
کارت ۲۴۸
پرسش
When can a regression relationship support a causal conclusion?
پاسخ
Only when the data come from a well-designed randomized experiment and the conclusion matches its scope.
کارت ۲۴۹
پرسش
What units does a residual use?
پاسخ
The same units as the response variable y.
کارت ۲۵۰
پرسش
What is an influential point in regression?
پاسخ
A point whose removal substantially changes the fitted regression line or another key regression result.
۲۵۰ کارت
AP Statistics Flashcards: Complete 5-Unit Course Review
Nibomo باز میشود تا بتوانید مطالعه را شروع کنید.