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