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