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