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