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