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