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