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