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