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