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