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.
حول هذه الرزمة
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.
بطاقات هذه الرزمة
البطاقة ١
السؤال
What makes a question a statistical investigative question?
الإجابة
It anticipates variability in data and can be answered by collecting and analyzing data about a population or process.
البطاقة ٢
السؤال
What is an observational unit?
الإجابة
An individual item or person from which data are collected.
البطاقة ٣
السؤال
A student's class year is recorded as freshman, sophomore, junior, or senior. What type of variable is this?
الإجابة
Categorical. The values name groups rather than measure a numerical amount.
البطاقة ٤
السؤال
How does a parameter differ from a statistic?
الإجابة
A parameter describes a population; a statistic describes a sample.
البطاقة ٥
السؤال
How is a category's relative frequency calculated?
الإجابة
Divide the category count by the total number of observations.
البطاقة ٦
السؤال
What should the height of a bar represent in a relative-frequency bar chart?
الإجابة
The proportion or percentage of observations in that category.
البطاقة ٧
السؤال
Number of text messages sent in a day: discrete or continuous?
الإجابة
Discrete. It is a count with separated possible values.
البطاقة ٨
السؤال
Which displays preserve individual quantitative data values?
الإجابة
Dotplots and stem-and-leaf plots. A histogram groups values into intervals.
البطاقة ٩
السؤال
What four features should a description of a quantitative distribution address?
الإجابة
Shape, center, variability, and unusual features such as gaps or outliers.
البطاقة ١٠
السؤال
Which measure of center is usually better for a strongly right-skewed distribution?
الإجابة
The median, because it is resistant to extreme high values.
البطاقة ١١
السؤال
The values are 3, 5, 5, and 11. What is the mean?
الإجابة
- The sum is 24, divided by 4 observations.
البطاقة ١٢
السؤال
The ordered values are 2, 4, 7, 9, 12, and 20. What is the median?
الإجابة
8, the average of the two middle values 7 and 9.
البطاقة ١٣
السؤال
How is the interquartile range calculated?
الإجابة
IQR = Q3 − Q1. It measures the spread of the middle 50% of the data.
البطاقة ١٤
السؤال
What does a small standard deviation say about a data set?
الإجابة
Values typically lie close to the mean.
البطاقة ١٥
السؤال
Which common summaries are resistant to extreme values?
الإجابة
The median and IQR are resistant; the mean and standard deviation are not.
البطاقة ١٦
السؤال
In a modified boxplot, where do the whiskers end?
الإجابة
At the smallest and largest observed values within the 1.5 × IQR fences; values beyond the fences are plotted separately as potential outliers.
البطاقة ١٧
السؤال
What are the 1.5 × IQR outlier fences?
الإجابة
Lower fence = Q1 − 1.5(IQR); upper fence = Q3 + 1.5(IQR). Values beyond them are flagged as potential outliers.
البطاقة ١٨
السؤال
How should two quantitative distributions be compared?
الإجابة
Compare shape, center, variability, and unusual features in context, using the same measure or display basis.
البطاقة ١٩
السؤال
What does a z-score of −1.8 mean?
الإجابة
The value is 1.8 standard deviations below the mean.
البطاقة ٢٠
السؤال
Every observation is converted from meters to centimeters by multiplying by 100. What happens to the mean and standard deviation?
الإجابة
Both are multiplied by 100.
البطاقة ٢١
السؤال
What should an investigative question identify so the conclusion has a clear scope?
الإجابة
The variable or parameter of interest and the population to which the conclusion may apply.
البطاقة ٢٢
السؤال
What is a census?
الإجابة
A study that collects data from every member of the population.
البطاقة ٢٣
السؤال
What makes a study an experiment?
الإجابة
Researchers deliberately assign treatments to experimental units.
البطاقة ٢٤
السؤال
How do prospective and retrospective observational studies differ?
الإجابة
A prospective study follows units forward and gathers future data; a retrospective study uses data from the past.
البطاقة ٢٥
السؤال
What is a confounding variable in an observational study?
الإجابة
A variable associated with both the explanatory and response variables that offers an alternative explanation for their relationship.
البطاقة ٢٦
السؤال
What study feature supports generalizing results to a population?
الإجابة
Random selection from that population.
البطاقة ٢٧
السؤال
What makes a study observational?
الإجابة
Researchers observe variables without assigning treatments.
البطاقة ٢٨
السؤال
What study feature supports a cause-and-effect conclusion?
الإجابة
Random assignment of treatments in a well-designed experiment.
البطاقة ٢٩
السؤال
What defines a simple random sample of size n?
الإجابة
Every possible sample of size n has the same chance of selection.
البطاقة ٣٠
السؤال
What changes when sampling is done with replacement?
الإجابة
A selected unit returns to the population and can be selected again.
البطاقة ٣١
السؤال
Why can a convenience sample be biased?
الإجابة
Easy-to-reach units may differ systematically from the target population.
البطاقة ٣٢
السؤال
Why should an experiment compare at least two treatment groups?
الإجابة
The comparison provides a baseline for judging whether responses differ by treatment.
البطاقة ٣٣
السؤال
A school samples 20 students at random from each grade. Which sampling method is this?
الإجابة
Stratified random sampling, with grade as the stratum.
البطاقة ٣٤
السؤال
What is the purpose of random assignment?
الإجابة
It tends to balance lurking variables across treatment groups, supporting causal inference.
البطاقة ٣٥
السؤال
Why can a voluntary-response sample be biased?
الإجابة
People with strong opinions are often more likely to participate.
البطاقة ٣٦
السؤال
What does replication mean in an experiment?
الإجابة
Assigning more than one experimental unit to each treatment so treatment differences can be separated from individual variability.
البطاقة ٣٧
السؤال
A city randomly selects 8 apartment buildings and surveys every household in those buildings. Which method is this?
الإجابة
Cluster random sampling.
البطاقة ٣٨
السؤال
What does direct control do in an experiment?
الإجابة
It holds potential extraneous sources of variation constant across experimental units.
البطاقة ٣٩
السؤال
What is undercoverage?
الإجابة
Some groups in the target population are left out of, or poorly represented in, the sampling frame.
البطاقة ٤٠
السؤال
What is the role of a control group?
الإجابة
It supplies a comparison condition for evaluating the treatment of interest.
البطاقة ٤١
السؤال
After a random start, a quality inspector checks every 40th item. Which sampling method is this?
الإجابة
Systematic random sampling.
البطاقة ٤٢
السؤال
Why might an experiment use a placebo?
الإجابة
To separate a treatment's effect from responses caused by expecting treatment.
البطاقة ٤٣
السؤال
What is nonresponse bias?
الإجابة
Selected individuals who do not respond differ in a relevant way from those who do.
البطاقة ٤٤
السؤال
What is single blinding designed to reduce?
الإجابة
Bias caused when participants or evaluators know which treatment was received, depending on who is blinded.
البطاقة ٤٥
السؤال
Why use a randomized block design?
الإجابة
To group units that are similar on an important source of variation, then compare treatments within each block.
البطاقة ٤٦
السؤال
What defines a matched-pairs design?
الإجابة
Two treatments are compared using paired similar units or by giving both treatments to each unit in randomized order.
البطاقة ٤٧
السؤال
A survey asks, “Don't you agree the new schedule is unfair?” What problem does this create?
الإجابة
Response bias from leading wording.
البطاقة ٤٨
السؤال
What usually makes an experiment double-blind?
الإجابة
Neither the participants nor the people evaluating responses know treatment assignments while outcomes are measured.
البطاقة ٤٩
السؤال
A researcher randomly assigns 80 volunteers to two diets and compares blood-pressure change. What conclusion can random assignment support?
الإجابة
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.
البطاقة ٥٠
السؤال
A researcher records coffee intake and sleep duration without assigning either. Can the study establish that coffee causes less sleep?
الإجابة
No. It is observational, so confounding can provide alternative explanations.
البطاقة ٥١
السؤال
What is the difference between a population and a sample?
الإجابة
The population is the full group of interest; a sample is the subset actually observed.
البطاقة ٥٢
السؤال
Which graph is appropriate for the distribution of one quantitative variable measured on 600 people?
الإجابة
A histogram is appropriate; it groups the many numerical values into intervals.
البطاقة ٥٣
السؤال
In a strongly right-skewed distribution, how do the mean and median usually compare?
الإجابة
The mean is usually larger because high values pull it to the right.
البطاقة ٥٤
السؤال
Every score increases by 7 points. What happens to the mean and standard deviation?
الإجابة
The mean increases by 7; the standard deviation stays unchanged.
البطاقة ٥٥
السؤال
What does it mean that a score is at the 80th percentile?
الإجابة
About 80% of scores are at or below it.
البطاقة ٥٦
السؤال
Why should gaps and clusters be mentioned when describing a distribution?
الإجابة
They may reveal distinct subgroups, collection effects, or other structure that center and spread alone hide.
البطاقة ٥٧
السؤال
What is the minimum ethical safeguard when collecting identifiable human data?
الإجابة
Obtain informed consent when required and protect participants' privacy and confidentiality.
البطاقة ٥٨
السؤال
Every measurement is multiplied by −2. What happens to the mean and standard deviation?
الإجابة
The mean is multiplied by −2; the standard deviation is multiplied by 2.
البطاقة ٥٩
السؤال
A study uses random sampling but no assigned treatment. What can it support?
الإجابة
Population generalization, but not a cause-and-effect conclusion.
البطاقة ٦٠
السؤال
A report calls any unmeasured variable a confounder. What is the correction?
الإجابة
A confounder must be related to both the explanatory and response variables and create an alternative explanation.
البطاقة ٦١
السؤال
What does a two-way table summarize?
الإجابة
Counts or relative frequencies for combinations of two categorical variables.
البطاقة ٦٢
السؤال
What is a joint relative frequency?
الإجابة
A cell count divided by the grand total, representing one combination of categories.
البطاقة ٦٣
السؤال
What is a marginal relative frequency?
الإجابة
A row or column total divided by the grand total.
البطاقة ٦٤
السؤال
How is a conditional relative frequency calculated within one row?
الإجابة
Divide each cell in that row by the row total.
البطاقة ٦٥
السؤال
What pattern suggests association between two categorical variables?
الإجابة
The conditional distribution of one variable changes across categories of the other.
البطاقة ٦٦
السؤال
Why are segmented bar charts useful for two categorical variables?
الإجابة
They place conditional distributions on the same 100% scale, making category patterns easy to compare.
البطاقة ٦٧
السؤال
How do an outcome and an event differ?
الإجابة
An outcome is one result of a trial; an event is a set of one or more outcomes.
البطاقة ٦٨
السؤال
What must a valid probability simulation specify?
الإجابة
A chance mechanism whose outcomes match the event probabilities, one trial definition, the statistic recorded, and many repetitions.
البطاقة ٦٩
السؤال
What does the law of large numbers predict?
الإجابة
As independent trials accumulate, an event's long-run relative frequency tends to approach its probability.
البطاقة ٧٠
السؤال
What two requirements must probabilities in a sample space satisfy?
الإجابة
Each probability is between 0 and 1, and the probabilities of all nonoverlapping outcomes sum to 1.
البطاقة ٧١
السؤال
What is the complement rule?
الإجابة
P(Aᶜ) = 1 − P(A). It is often useful for “at least one” events.
البطاقة ٧٢
السؤال
How can you verify that events A and B are mutually exclusive?
الإجابة
Their intersection is impossible, so P(A ∩ B) = 0.
البطاقة ٧٣
السؤال
What is the formula for P(A | B), when P(B) > 0?
الإجابة
P(A | B) = P(A ∩ B) / P(B). The restricted sample space is B.
البطاقة ٧٤
السؤال
What is the general multiplication rule for two events?
الإجابة
P(A ∩ B) = P(A)P(B | A), or equivalently P(B)P(A | B).
البطاقة ٧٥
السؤال
What does it mean for events A and B to be independent?
الإجابة
Knowing that one occurred does not change the probability of the other.
البطاقة ٧٦
السؤال
What is the general addition rule?
الإجابة
P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
البطاقة ٧٧
السؤال
Why are two mutually exclusive events with positive probabilities not independent?
الإجابة
If one occurs, the other cannot occur, so its conditional probability drops to 0.
البطاقة ٧٨
السؤال
What is a random variable?
الإجابة
A numerical value determined by the outcome of a random process.
البطاقة ٧٩
السؤال
What makes a table a valid discrete probability distribution?
الإجابة
It lists every possible value with probabilities from 0 to 1 that sum to 1.
البطاقة ٨٠
السؤال
What does a cumulative distribution value F(x) represent?
الإجابة
P(X ≤ x), the probability that the random variable is at most x.
البطاقة ٨١
السؤال
How is the expected value of a discrete random variable calculated?
الإجابة
Multiply each possible value by its probability and add: E(X) = ΣxP(X = x).
البطاقة ٨٢
السؤال
What does the standard deviation of a random variable measure?
الإجابة
The typical distance of long-run outcomes from the random variable's mean.
البطاقة ٨٣
السؤال
How is the standard deviation of a discrete random variable calculated?
الإجابة
σₓ = √[Σ(x − μₓ)²P(X = x)]. The quantity inside the square root is Var(X).
البطاقة ٨٤
السؤال
A game has E(X) = −$0.40 per play. What does this mean?
الإجابة
Over many plays, the player's average net result approaches a loss of 40 cents per play; it does not predict every play.
البطاقة ٨٥
السؤال
What conditions define a binomial random variable?
الإجابة
A fixed number of independent trials, two outcomes per trial, constant success probability, and X counts successes.
البطاقة ٨٦
السؤال
For X ~ Binomial(n, p), what are the mean and standard deviation?
الإجابة
Mean = np; standard deviation = √[np(1 − p)].
البطاقة ٨٧
السؤال
For X ~ Binomial(n, p), what is P(X = x)?
الإجابة
Choose x success positions, then multiply: C(n, x)pˣ(1 − p)ⁿ⁻ˣ.
البطاقة ٨٨
السؤال
How can P(X ≥ 1) be found efficiently for a binomial variable?
الإجابة
Use the complement: P(X ≥ 1) = 1 − P(X = 0).
البطاقة ٨٩
السؤال
What should one simulated trial represent when estimating P(X ≥ 4) for X ~ Binomial(10, 0.3)?
الإجابة
Ten independent success/failure observations with success probability 0.3, followed by recording whether at least four successes occurred.
البطاقة ٩٠
السؤال
What features characterize a normal distribution?
الإجابة
It is continuous, symmetric, unimodal, and bell-shaped.
البطاقة ٩١
السؤال
Which parameters determine a normal distribution?
الإجابة
Its mean μ sets the center, and its standard deviation σ sets the spread.
البطاقة ٩٢
السؤال
What is the standard normal distribution?
الإجابة
The normal distribution with mean 0 and standard deviation 1.
البطاقة ٩٣
السؤال
What is the 68–95–99.7 rule?
الإجابة
For an approximately normal distribution, about 68%, 95%, and 99.7% of values lie within 1, 2, and 3 standard deviations of the mean.
البطاقة ٩٤
السؤال
What does an area under a normal curve represent?
الإجابة
The probability or population proportion within the corresponding interval.
البطاقة ٩٥
السؤال
How do you find the value cutting off the lowest 10% of a normal distribution?
الإجابة
Find the z-score with cumulative area 0.10, then convert with x = μ + zσ.
البطاقة ٩٦
السؤال
A normal variable has μ = 50 and σ = 8. What z-score corresponds to x = 62?
الإجابة
1.5, because z = (62 − 50) / 8.
البطاقة ٩٧
السؤال
Two exam scores come from different normal distributions. What makes their percentiles comparable?
الإجابة
Standardize each score with its own distribution's mean and standard deviation, then compare z-scores or cumulative areas.
البطاقة ٩٨
السؤال
What is a sampling distribution of a statistic?
الإجابة
The distribution of that statistic over all possible random samples of a fixed size from a population.
البطاقة ٩٩
السؤال
How can a sampling distribution be approximated by simulation?
الإجابة
Repeatedly take random samples of the same size, calculate the statistic each time, and graph the resulting values.
البطاقة ١٠٠
السؤال
What is a randomization distribution?
الإجابة
A simulated distribution of a statistic produced by repeatedly reallocating responses or labels as specified by a null model.
البطاقة ١٠١
السؤال
What does the central limit theorem say about sample means?
الإجابة
For random samples, the sampling distribution of the sample mean becomes approximately normal as sample size grows, even when the population is not normal.
البطاقة ١٠٢
السؤال
How does increasing sample size affect the normal approximation in the central limit theorem?
الإجابة
It generally improves the approximation, especially for skewed or irregular populations.
البطاقة ١٠٣
السؤال
A segmented bar chart shows nearly identical category proportions for every group. What does that suggest?
الإجابة
Little or no association between the two categorical variables.
البطاقة ١٠٤
السؤال
In a survey, 30 of 120 students both bike to school and arrive before 8:00. What is the joint relative frequency?
الإجابة
0.25, because 30 / 120 = 0.25.
البطاقة ١٠٥
السؤال
Why can P(A | B) differ from P(B | A)?
الإجابة
They use different restricted sample spaces and usually have different denominators.
البطاقة ١٠٦
السؤال
If P(A) = 0.4 and P(A | B) = 0.4 with P(B) > 0, what does this indicate?
الإجابة
A and B are independent because learning B does not change the probability of A.
البطاقة ١٠٧
السؤال
If independent events have probabilities 0.6 and 0.5, what is the probability that both occur?
الإجابة
0.30, using P(A ∩ B) = P(A)P(B).
البطاقة ١٠٨
السؤال
A prize is $0 with probability 0.7 and $10 with probability 0.3. What is the expected prize?
الإجابة
$3, because 0(0.7) + 10(0.3) = 3.
البطاقة ١٠٩
السؤال
A machine produces defective items independently with probability 0.02. What distribution models the number of defectives in 50 items?
الإجابة
Binomial with n = 50 and p = 0.02.
البطاقة ١١٠
السؤال
Heights are approximately normal with μ = 170 cm and σ = 6 cm. About what percent lie from 158 to 182 cm?
الإجابة
About 95%, because the interval is μ ± 2σ.
البطاقة ١١١
السؤال
What makes an estimator unbiased?
الإجابة
Its sampling distribution is centered at the population parameter it estimates.
البطاقة ١١٢
السؤال
For random samples of size n, what is the mean of the sampling distribution of p̂?
الإجابة
μₚ̂ = p, where p is the population proportion.
البطاقة ١١٣
السؤال
Which procedure estimates one population proportion from a random sample?
الإجابة
A one-sample z-interval for a population proportion.
البطاقة ١١٤
السؤال
How should a confidence interval for a population proportion be interpreted?
الإجابة
We are confident at the stated level that the interval captures the true population proportion, in context.
البطاقة ١١٥
السؤال
What hypotheses test whether a population proportion differs from 0.40?
الإجابة
H₀: p = 0.40 versus Hₐ: p ≠ 0.40.
البطاقة ١١٦
السؤال
What is a p-value?
الإجابة
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.
البطاقة ١١٧
السؤال
What is the hypothesis-test decision rule using significance level α?
الإجابة
Reject H₀ when the p-value ≤ α; otherwise fail to reject H₀.
البطاقة ١١٨
السؤال
What is a Type I error?
الإجابة
Rejecting H₀ when H₀ is actually true.
البطاقة ١١٩
السؤال
What is the mean of p̂₁ − p̂₂ for independent random samples?
الإجابة
p₁ − p₂.
البطاقة ١٢٠
السؤال
Which procedure estimates p₁ − p₂ from two independent samples or randomized groups?
الإجابة
A two-sample z-interval for a difference between population proportions.
البطاقة ١٢١
السؤال
How should a confidence interval for p₁ − p₂ be interpreted?
الإجابة
We are confident at the stated level that the interval captures the true difference p₁ − p₂, in context.
البطاقة ١٢٢
السؤال
What null hypothesis is standard when testing whether two population proportions differ?
الإجابة
H₀: p₁ − p₂ = 0, equivalently p₁ = p₂.
البطاقة ١٢٣
السؤال
A two-proportion test gives p-value 0.018 at α = 0.05. What decision follows?
الإجابة
Reject H₀ because 0.018 < 0.05.
البطاقة ١٢٤
السؤال
When is a chi-square test for independence appropriate?
الإجابة
When one random sample provides two categorical variables and the question asks whether they are associated in one population.
البطاقة ١٢٥
السؤال
How should a chi-square test p-value be interpreted?
الإجابة
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.
٢٥٠ بطاقة
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البطاقة ١٢٦
السؤال
How do bias and variability differ for an estimator?
الإجابة
Bias concerns where the sampling distribution is centered; variability concerns how spread out it is.
البطاقة ١٢٧
السؤال
What is the standard deviation of p̂ when observations are independent?
الإجابة
σₚ̂ = √[p(1 − p) / n].
البطاقة ١٢٨
السؤال
What is the one-proportion z-interval formula?
الإجابة
p̂ ± z*√[p̂(1 − p̂) / n].
البطاقة ١٢٩
السؤال
What does a 95% confidence level describe?
الإجابة
In repeated random sampling with the same method, about 95% of the resulting intervals would capture the true parameter.
البطاقة ١٣٠
السؤال
Which method tests a claim about one population proportion when its conditions hold?
الإجابة
A one-sample z-test for a population proportion.
البطاقة ١٣١
السؤال
How does the alternative hypothesis determine a p-value's tail area?
الإجابة
A greater-than alternative uses the upper tail, a less-than alternative uses the lower tail, and a not-equal alternative uses both tails.
البطاقة ١٣٢
السؤال
What wording should follow a rejected null hypothesis?
الإجابة
There is convincing statistical evidence for the alternative claim about the population parameter, stated in context.
البطاقة ١٣٣
السؤال
What is a Type II error?
الإجابة
Failing to reject H₀ when Hₐ is actually true.
البطاقة ١٣٤
السؤال
What is the standard deviation of p̂₁ − p̂₂ for independent samples?
الإجابة
√[p₁(1 − p₁)/n₁ + p₂(1 − p₂)/n₂].
البطاقة ١٣٥
السؤال
What standard error is used in a confidence interval for p₁ − p₂?
الإجابة
√[p̂₁(1 − p̂₁)/n₁ + p̂₂(1 − p̂₂)/n₂]; the sample proportions are not pooled.
البطاقة ١٣٦
السؤال
A confidence interval for p₁ − p₂ contains 0. What does that imply?
الإجابة
The interval does not provide convincing evidence of a difference between the population proportions at the corresponding two-sided significance level.
البطاقة ١٣٧
السؤال
Why is a pooled proportion used in a two-proportion z-test with H₀: p₁ = p₂?
الإجابة
The null model assumes both samples share one common population proportion, estimated by combining successes and observations.
البطاقة ١٣٨
السؤال
How should a p-value for a two-proportion test be stated?
الإجابة
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.
البطاقة ١٣٩
السؤال
When is a chi-square test for homogeneity appropriate?
الإجابة
When independent samples or randomized groups are compared on the distribution of one categorical response variable.
البطاقة ١٤٠
السؤال
What is the chi-square test statistic formula?
الإجابة
χ² = Σ[(observed − expected)² / expected], summed over all cells.
البطاقة ١٤١
السؤال
What usually happens to an estimator's sampling variability as sample size increases?
الإجابة
It decreases; estimates from larger random samples tend to cluster more tightly around the parameter.
البطاقة ١٤٢
السؤال
When is the sampling distribution of p̂ approximately normal?
الإجابة
When the expected counts np and n(1 − p) are both at least 10.
البطاقة ١٤٣
السؤال
What conditions justify a one-proportion z-interval?
الإجابة
Random data; independence, checked with n ≤ 10% of the population when sampling without replacement; and at least 10 observed successes and 10 observed failures.
البطاقة ١٤٤
السؤال
A 95% confidence interval for p is (0.52, 0.61). What does it say about the claim p = 0.50?
الإجابة
The interval excludes 0.50, so the data provide evidence against p = 0.50 in a two-sided test at α = 0.05.
البطاقة ١٤٥
السؤال
What is the one-proportion z-test statistic?
الإجابة
z = (p̂ − p₀) / √[p₀(1 − p₀)/n], using the null proportion p₀ in the standard error.
البطاقة ١٤٦
السؤال
How is a simulation-based p-value estimated?
الإجابة
Find the proportion of simulated null statistics at least as extreme as the observed statistic in the direction of Hₐ.
البطاقة ١٤٧
السؤال
What does “fail to reject H₀” mean?
الإجابة
The data do not provide convincing evidence for Hₐ; it does not prove H₀ true.
البطاقة ١٤٨
السؤال
With sample size and effect fixed, what often happens when α is lowered?
الإجابة
The chance of a Type I error decreases, while the chance of a Type II error increases.
البطاقة ١٤٩
السؤال
What conditions support the usual model for p̂₁ − p̂₂?
الإجابة
Independent random samples or randomized groups, independence within each group, and large enough expected success and failure counts for normal approximation.
البطاقة ١٥٠
السؤال
What conditions justify a two-proportion z-interval?
الإجابة
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.
البطاقة ١٥١
السؤال
How does increasing both sample sizes affect a confidence interval for p₁ − p₂?
الإجابة
It reduces the standard error and usually narrows the interval when other factors stay the same.
البطاقة ١٥٢
السؤال
What standard error is used in the two-proportion z-test?
الإجابة
√[p̂c(1 − p̂c)(1/n₁ + 1/n₂)], where p̂c is the pooled sample proportion.
البطاقة ١٥٣
السؤال
A randomized experiment uses volunteers assigned to two treatments. A significant two-proportion test supports what scope?
الإجابة
A cause-and-effect conclusion for people similar to the volunteers, not automatic generalization to a broader population.
البطاقة ١٥٤
السؤال
How is an expected count computed in a two-way table under independence?
الإجابة
Expected count = (row total × column total) / grand total.
البطاقة ١٥٥
السؤال
What conditions justify a chi-square test for a two-way table?
الإجابة
Random data; independent observations, including the 10% check when sampling without replacement; and every expected cell count greater than 5.
البطاقة ١٥٦
السؤال
A sampling distribution is centered away from the true parameter. What problem does this reveal?
الإجابة
Bias in the estimator.
البطاقة ١٥٧
السؤال
If p = 0.30 and n = 100, what does μₚ̂ = 0.30 mean?
الإجابة
Across many random samples of 100, the average sample proportion would be 0.30.
البطاقة ١٥٨
السؤال
For a planned proportion interval with margin of error m, what conservative p-value is used when no prior estimate exists?
الإجابة
Use p* = 0.50 in n ≥ (z*/m)²p*(1 − p*) because it gives the largest required sample size.
البطاقة ١٥٩
السؤال
What two changes widen a confidence interval for a proportion?
الإجابة
Using a higher confidence level or a smaller sample size.
البطاقة ١٦٠
السؤال
Which counts check normality for a one-proportion z-test?
الإجابة
Use the null model: np₀ ≥ 10 and n(1 − p₀) ≥ 10.
البطاقة ١٦١
السؤال
What is wrong with saying “the p-value is the probability that H₀ is true”?
الإجابة
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.
البطاقة ١٦٢
السؤال
What does “statistically significant at α = 0.01” mean?
الإجابة
The p-value is at most 0.01, so H₀ is rejected at that significance level.
البطاقة ١٦٣
السؤال
What is the power of a hypothesis test?
الإجابة
The probability that the test rejects H₀ when a particular alternative is true.
البطاقة ١٦٤
السؤال
If p₁ = p₂, where is the sampling distribution of p̂₁ − p̂₂ centered?
الإجابة
At 0, because its mean is p₁ − p₂.
البطاقة ١٦٥
السؤال
Why must the order p̂₁ − p̂₂ stay consistent throughout an interval?
الإجابة
Changing the order reverses the sign and changes the contextual interpretation of every endpoint.
البطاقة ١٦٦
السؤال
A 95% interval for p₁ − p₂ is (0.04, 0.15). What conclusion is supported?
الإجابة
p₁ is plausibly 0.04 to 0.15 higher than p₂; the interval supports a positive difference.
البطاقة ١٦٧
السؤال
Which success-failure counts are checked for a two-proportion z-test?
الإجابة
Expected counts based on the pooled null proportion: n₁p̂c, n₁(1 − p̂c), n₂p̂c, and n₂(1 − p̂c), each at least 10.
البطاقة ١٦٨
السؤال
A two-proportion test with Hₐ: p₁ ≠ p₂ fails to reject H₀. What conclusion is valid?
الإجابة
There is not convincing evidence that the two population proportions differ.
البطاقة ١٦٩
السؤال
What are the degrees of freedom for a chi-square test on an r × c table?
الإجابة
(r − 1)(c − 1).
البطاقة ١٧٠
السؤال
A chi-square test for independence has a small p-value. What conclusion is appropriate?
الإجابة
There is convincing evidence of an association between the two categorical variables in the population, stated in context.
البطاقة ١٧١
السؤال
What is the mean of the sampling distribution of x̄ for random samples from a population with mean μ?
الإجابة
μₓ̄ = μ.
البطاقة ١٧٢
السؤال
Which procedure estimates one population mean when the population standard deviation is unknown?
الإجابة
A one-sample t-interval for a population mean.
البطاقة ١٧٣
السؤال
How should a confidence interval for a population mean be interpreted?
الإجابة
We are confident at the stated level that the interval captures the true population mean, in context.
البطاقة ١٧٤
السؤال
What hypotheses test whether a population mean exceeds 12?
الإجابة
H₀: μ = 12 versus Hₐ: μ > 12.
البطاقة ١٧٥
السؤال
A one-sample t-test gives p-value 0.08 at α = 0.05. What decision follows?
الإجابة
Fail to reject H₀ because 0.08 > 0.05.
البطاقة ١٧٦
السؤال
What is the mean of x̄₁ − x̄₂ for independent random samples?
الإجابة
μ₁ − μ₂.
البطاقة ١٧٧
السؤال
Which procedure estimates μ₁ − μ₂ from two independent samples?
الإجابة
A two-sample t-interval for a difference between population means.
البطاقة ١٧٨
السؤال
How should a confidence interval for μ₁ − μ₂ be interpreted?
الإجابة
We are confident at the stated level that the interval captures the true difference μ₁ − μ₂, in context.
البطاقة ١٧٩
السؤال
What null hypothesis is standard when testing whether two population means differ?
الإجابة
H₀: μ₁ − μ₂ = 0, equivalently μ₁ = μ₂.
البطاقة ١٨٠
السؤال
A two-sample t-test gives p-value 0.004 at α = 0.01. What decision follows?
الإجابة
Reject H₀ because 0.004 < 0.01.
البطاقة ١٨١
السؤال
What is the standard deviation of x̄ when observations are independent?
الإجابة
σₓ̄ = σ / √n.
البطاقة ١٨٢
السؤال
What is the one-sample t-interval formula for μ?
الإجابة
x̄ ± t* × s/√n, with t* based on n − 1 degrees of freedom.
البطاقة ١٨٣
السؤال
What does a 90% confidence level mean for a mean interval procedure?
الإجابة
Across many random samples using the same procedure, about 90% of the intervals would capture the true population mean.
البطاقة ١٨٤
السؤال
Which procedure tests a claim about one population mean when σ is unknown?
الإجابة
A one-sample t-test for a population mean.
البطاقة ١٨٥
السؤال
How should a one-mean test p-value be interpreted?
الإجابة
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.
البطاقة ١٨٦
السؤال
What is the standard deviation of x̄₁ − x̄₂ for independent samples?
الإجابة
√(σ₁²/n₁ + σ₂²/n₂).
البطاقة ١٨٧
السؤال
What standard error is used in a two-sample t-interval for μ₁ − μ₂?
الإجابة
√(s₁²/n₁ + s₂²/n₂).
البطاقة ١٨٨
السؤال
A confidence interval for μ₁ − μ₂ contains 0. What does that imply?
الإجابة
The interval does not provide convincing evidence of a difference between the population means at the corresponding two-sided significance level.
البطاقة ١٨٩
السؤال
What is the two-sample t-statistic for testing H₀: μ₁ − μ₂ = 0?
الإجابة
t = [(x̄₁ − x̄₂) − 0] / √(s₁²/n₁ + s₂²/n₂).
البطاقة ١٩٠
السؤال
How should a two-mean test p-value be interpreted?
الإجابة
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.
البطاقة ١٩١
السؤال
When is the sampling distribution of x̄ approximately normal?
الإجابة
When the population is approximately normal or the random sample is large enough for the central limit theorem to apply.
البطاقة ١٩٢
السؤال
What conditions justify a one-sample t-interval?
الإجابة
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.
البطاقة ١٩٣
السؤال
How does increasing sample size affect a confidence interval for μ?
الإجابة
It lowers the standard error and usually narrows the interval when confidence level and variability stay comparable.
البطاقة ١٩٤
السؤال
What is the one-sample t-test statistic?
الإجابة
t = (x̄ − μ₀) / (s/√n), with n − 1 degrees of freedom.
البطاقة ١٩٥
السؤال
A t-test fails to reject H₀. What should the conclusion avoid?
الإجابة
Avoid saying H₀ is true; say the data do not provide convincing evidence for Hₐ.
البطاقة ١٩٦
السؤال
When is x̄₁ − x̄₂ approximately normal?
الإجابة
When both populations are approximately normal or both independent random samples are large enough for normal approximations.
البطاقة ١٩٧
السؤال
What conditions justify a two-sample t-interval?
الإجابة
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.
البطاقة ١٩٨
السؤال
A 95% interval for μ₁ − μ₂ is (−7.2, −1.4). What does it support?
الإجابة
μ₁ is plausibly 1.4 to 7.2 units lower than μ₂; the interval supports a negative difference.
البطاقة ١٩٩
السؤال
What sample-shape condition is checked for a two-sample t-test with small samples?
الإجابة
Both sample distributions should be free of strong skewness and outliers unless both populations are known to be approximately normal.
البطاقة ٢٠٠
السؤال
A randomized experiment finds a significant difference in mean response. What can random assignment support?
الإجابة
A cause-and-effect conclusion for units like those studied, assuming the experiment was well designed.
البطاقة ٢٠١
السؤال
A population has μ = 40. What does μₓ̄ = 40 mean for samples of size 25?
الإجابة
Across all random samples of 25, the average sample mean is 40.
البطاقة ٢٠٢
السؤال
How is a matched-pairs confidence interval analyzed?
الإجابة
Compute one difference for each pair, then use a one-sample t-interval on the population mean difference.
البطاقة ٢٠٣
السؤال
A 95% confidence interval for μ is (18.2, 21.7). What does it say about μ = 22?
الإجابة
The interval excludes 22, providing evidence against μ = 22 in a two-sided test at α = 0.05.
البطاقة ٢٠٤
السؤال
Which observations enter a matched-pairs t-test?
الإجابة
The within-pair differences, not the two original columns treated as independent samples.
البطاقة ٢٠٥
السؤال
A test reports p-value 0.032. At which common levels is it significant: 0.05 or 0.01?
الإجابة
Significant at 0.05, but not at 0.01.
البطاقة ٢٠٦
السؤال
If μ₁ − μ₂ = 5, where is the sampling distribution of x̄₁ − x̄₂ centered?
الإجابة
At 5.
البطاقة ٢٠٧
السؤال
Does the standard AP two-sample t procedure require equal population variances?
الإجابة
No. It uses separate sample variances in the standard error rather than pooling them.
البطاقة ٢٠٨
السؤال
What two changes usually widen a confidence interval for μ₁ − μ₂?
الإجابة
Higher confidence or smaller sample sizes.
البطاقة ٢٠٩
السؤال
Why must the order x̄₁ − x̄₂ match the order μ₁ − μ₂ in the hypotheses?
الإجابة
Reversing the order reverses the sign and changes the direction of the claim.
البطاقة ٢١٠
السؤال
A two-sample test with Hₐ: μ₁ > μ₂ fails to reject H₀. What conclusion is valid?
الإجابة
There is not convincing evidence that μ₁ exceeds μ₂.
البطاقة ٢١١
السؤال
A population has σ = 18 and random samples have n = 36. What is σₓ̄?
الإجابة
3, because 18/√36 = 3.
البطاقة ٢١٢
السؤال
Why is a t distribution used for inference about a mean when σ is unknown?
الإجابة
Replacing σ with the sample standard deviation s adds uncertainty, which the heavier-tailed t distribution accounts for.
البطاقة ٢١٣
السؤال
What conditions justify a one-sample t-test?
الإجابة
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.
البطاقة ٢١٤
السؤال
What distinguishes a two-sample means procedure from a matched-pairs procedure?
الإجابة
Two-sample procedures use independent groups; matched-pairs procedures analyze linked observations through their differences.
البطاقة ٢١٥
السؤال
How are degrees of freedom handled for a two-sample t procedure?
الإجابة
Technology usually uses an approximation based on both sample variances and sizes; a conservative fallback uses the smaller of n₁ − 1 and n₂ − 1.
البطاقة ٢١٦
السؤال
What type of variables belong on a scatterplot?
الإجابة
Two quantitative variables measured on the same observational units.
البطاقة ٢١٧
السؤال
What does the correlation coefficient r describe?
الإجابة
The direction and strength of a linear relationship between two quantitative variables.
البطاقة ٢١٨
السؤال
What does ŷ = a + bx represent?
الإجابة
A linear regression model predicting response y from explanatory variable x.
البطاقة ٢١٩
السؤال
What is a residual?
الإجابة
Observed response minus predicted response: residual = y − ŷ.
البطاقة ٢٢٠
السؤال
What makes a regression line the least-squares line?
الإجابة
It minimizes the sum of squared residuals.
البطاقة ٢٢١
السؤال
What four features should a scatterplot description address?
الإجابة
Direction, form, strength, and unusual features such as outliers or clusters.
البطاقة ٢٢٢
السؤال
What values can r take?
الإجابة
Any value from −1 to 1, inclusive.
البطاقة ٢٢٣
السؤال
How is the slope b interpreted in context?
الإجابة
For each one-unit increase in x, the predicted value of y changes by b units on average.
البطاقة ٢٢٤
السؤال
What does a positive residual mean?
الإجابة
The observed response is above the model's predicted response.
البطاقة ٢٢٥
السؤال
What is the least-squares slope formula?
الإجابة
b = r(sᵧ/sₓ).
البطاقة ٢٢٦
السؤال
A scatterplot trends downward from left to right. What direction is the association?
الإجابة
Negative: larger x-values tend to occur with smaller y-values.
البطاقة ٢٢٧
السؤال
Why can r be near 0 even when two variables are strongly related?
الإجابة
Correlation measures only linear association, so a strong curved relationship can have r near 0.
البطاقة ٢٢٨
السؤال
How is the intercept a interpreted in context?
الإجابة
It is the predicted response when x = 0, provided x = 0 is meaningful and within the data's scope.
البطاقة ٢٢٩
السؤال
A model predicts 18, and the observed response is 21. What is the residual?
الإجابة
3, because 21 − 18 = 3.
البطاقة ٢٣٠
السؤال
How is the least-squares intercept found from the slope?
الإجابة
a = ȳ − bx̄.
البطاقة ٢٣١
السؤال
What makes a linear association look strong?
الإجابة
The points lie close to a straight-line pattern, regardless of whether the slope is steep or shallow.
البطاقة ٢٣٢
السؤال
Does r have measurement units?
الإجابة
No. Correlation is unitless because it is based on standardized values.
البطاقة ٢٣٣
السؤال
For ŷ = 12 + 2.5x, what is predicted when x = 4?
الإجابة
22, because 12 + 2.5(4) = 22.
البطاقة ٢٣٤
السؤال
What residual-plot pattern supports using a linear model?
الإجابة
Random scatter around zero with no clear curve, trend, or changing spread.
البطاقة ٢٣٥
السؤال
What does r² measure in simple linear regression?
الإجابة
The proportion of variation in the response variable explained by its linear relationship with the explanatory variable.
البطاقة ٢٣٦
السؤال
A scatterplot shows a strong association. Does that establish causation?
الإجابة
No. A scatterplot alone cannot rule out confounding or other explanations.
البطاقة ٢٣٧
السؤال
Why should unusual points be checked before interpreting r?
الإجابة
Correlation is not resistant; an outlier or influential point can change r substantially.
البطاقة ٢٣٨
السؤال
Why is extrapolation risky?
الإجابة
The relationship observed over the data range may not continue beyond that range.
البطاقة ٢٣٩
السؤال
A point lies below the regression line. What sign is its residual?
الإجابة
Negative, because observed y is less than predicted ŷ.
البطاقة ٢٤٠
السؤال
Which point always lies on a least-squares regression line with an intercept?
الإجابة
The point (x̄, ȳ).
البطاقة ٢٤١
السؤال
Which variable goes on each axis of a scatterplot used for prediction?
الإجابة
The explanatory variable goes on the horizontal x-axis; the response variable goes on the vertical y-axis.
البطاقة ٢٤٢
السؤال
What happens to r if the roles of x and y are swapped?
الإجابة
Nothing. Correlation is symmetric.
البطاقة ٢٤٣
السؤال
What is interpolation?
الإجابة
Predicting a response for an x-value within the range of observed explanatory values.
البطاقة ٢٤٤
السؤال
A residual plot has a clear U-shape. What is the correction?
الإجابة
Do not treat the linear model as adequate; the curved pattern shows systematic structure remains.
البطاقة ٢٤٥
السؤال
A regression has r² = 0.64. What does this mean?
الإجابة
About 64% of the variation in the response is explained by its linear relationship with the explanatory variable.
البطاقة ٢٤٦
السؤال
What is an outlier in a scatterplot?
الإجابة
A point that falls away from the overall pattern of the other points.
البطاقة ٢٤٧
السؤال
What happens to r when x is converted from centimeters to meters?
الإجابة
It stays the same because multiplying by a positive constant does not change standardized linear association.
البطاقة ٢٤٨
السؤال
When can a regression relationship support a causal conclusion?
الإجابة
Only when the data come from a well-designed randomized experiment and the conclusion matches its scope.
البطاقة ٢٤٩
السؤال
What units does a residual use?
الإجابة
The same units as the response variable y.
البطاقة ٢٥٠
السؤال
What is an influential point in regression?
الإجابة
A point whose removal substantially changes the fitted regression line or another key regression result.
٢٥٠ بطاقة
AP Statistics Flashcards: Complete 5-Unit Course Review
سيفتح تطبيق Flashcards لتبدأ الدراسة.