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