AP Statistics Flashcards: Inference And Experiments

What this deck covers

This deck focuses on Inference And Experiments, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the effect of increasing sample size on margin of error?

Answer: Decreases the margin of error. Larger samples provide more precise estimates.

Flashcard 2: Define 'standard deviation'.

Answer: Measure of data dispersion around the mean. Quantifies how spread out data points are.

Flashcard 3: What is a 'confidence interval'?

Answer: Range of values likely to contain a population parameter. Provides an estimate with associated uncertainty.

Flashcard 4: Define 'observational study'.

Answer: Study observing subjects without manipulation or intervention. Cannot establish causation, only association.

Flashcard 5: Which design reduces variability by pairing similar subjects?

Answer: Matched pairs design. Effective method for controlling individual differences.

Flashcard 6: What is a Type I error?

Answer: Rejecting a true null hypothesis. A false positive error with probability $\alpha$.

Flashcard 7: Identify the null hypothesis symbol.

Answer: $H_0$. Standard notation for the null hypothesis in statistics.

Flashcard 8: What is the 'central limit theorem'?

Answer: Distribution of sample means approximates normality as sample size increases. Foundation for statistical inference with large samples.

Flashcard 9: Identify the alternative hypothesis symbol.

Answer: $H_a$. Standard notation for the alternative hypothesis in statistics.

Flashcard 10: What is 'stratified sampling'?

Answer: Dividing population into subgroups and sampling each proportionally. Ensures all subgroups are adequately represented.

Flashcard 11: What does 'random sampling' ensure?

Answer: Each member of the population has an equal chance of selection. Eliminates selection bias and enables valid inference.

Flashcard 12: What is 'confounding'?

Answer: Distortion of the effect of one variable due to another. Makes it difficult to isolate the true effect.

Flashcard 13: Define 'systematic sampling'.

Answer: Selecting every nth member from a list after a random start. Simple method but may introduce patterns or bias.

Flashcard 14: What is the 'law of large numbers'?

Answer: As sample size increases, sample mean approaches population mean. Foundation for probability and statistical inference.

Flashcard 15: What is a Type II error?

Answer: Failing to reject a false null hypothesis. A false negative error with probability $\beta$.

Flashcard 16: What does 'internal validity' refer to?

Answer: Extent to which cause-and-effect conclusions are warranted. Focuses on the accuracy of causal inferences.

Flashcard 17: Which test is used for comparing means of two groups?

Answer: $t$-test. Uses the $t$-distribution when population standard deviation is unknown.

Flashcard 18: State the significance level symbol.

Answer: $\text{alpha}$ or $\text{α}$. Greek letter alpha represents the significance threshold.

Flashcard 19: What is a 'matched pairs design'?

Answer: Pairs of similar subjects receive different treatments for comparison. Controls for individual differences between subjects.

Flashcard 20: Define 'observational study'.

Answer: Study observing subjects without manipulation or intervention. Cannot establish causation, only association.

Flashcard 21: Define 'power of a test'.

Answer: Probability of correctly rejecting a false null hypothesis. Power equals $1 - \beta$ where $\beta$ is Type II error rate.

Flashcard 22: State one advantage of stratified sampling.

Answer: Ensures representation of all subgroups in the sample. Particularly useful when subgroups differ significantly.

Flashcard 23: Define a 'control group' in an experiment.

Answer: A group that does not receive the treatment, used for comparison. Provides a baseline to measure treatment effects against.

Flashcard 24: Which measure indicates the center of a data set?

Answer: Mean or median. Describes the central tendency of the distribution.

Flashcard 25: What is 'bias' in statistical studies?

Answer: Systematic error leading to incorrect conclusions. Can occur in sampling, measurement, or analysis.

Flashcard 26: Define a 'control group' in an experiment.

Answer: A group that does not receive the treatment, used for comparison. Provides a baseline to measure treatment effects against.

Flashcard 27: What does 'external validity' refer to?

Answer: Extent to which results generalize to other contexts. Relates to the generalizability of study findings.

Flashcard 28: What does 'external validity' refer to?

Answer: Extent to which results generalize to other contexts. Relates to the generalizability of study findings.

Flashcard 29: What does 'statistical significance' mean?

Answer: A result unlikely to occur by chance alone, below a threshold $p$-value. Indicates the result is not likely due to random variation.

Flashcard 30: Which measure indicates the center of a data set?

Answer: Mean or median. Describes the central tendency of the distribution.

Flashcard 31: Which test is used for comparing means of two groups?

Answer: $t$-test. Uses the $t$-distribution when population standard deviation is unknown.

Flashcard 32: What is a 'p-value'?

Answer: Probability of observing data at least as extreme under $H_0$. Measures evidence against the null hypothesis.

Flashcard 33: What is 'bias' in statistical studies?

Answer: Systematic error leading to incorrect conclusions. Can occur in sampling, measurement, or analysis.

Flashcard 34: What is the 'central limit theorem'?

Answer: Distribution of sample means approximates normality as sample size increases. Foundation for statistical inference with large samples.

Flashcard 35: State the significance level symbol.

Answer: $\text{alpha}$ or $\text{α}$. Greek letter alpha represents the significance threshold.

Flashcard 36: What is the purpose of a placebo?

Answer: To account for the placebo effect in experiments. Controls for psychological effects of receiving treatment.

Flashcard 37: What is a 'matched pairs design'?

Answer: Pairs of similar subjects receive different treatments for comparison. Controls for individual differences between subjects.

Flashcard 38: Which test compares proportions?

Answer: Chi-square test. Tests independence or goodness of fit for categorical data.

Flashcard 39: What is the primary goal of randomization?

Answer: To reduce bias and confounding in the experiment. Creates comparable groups and eliminates systematic differences.

Flashcard 40: Name the test for examining relationships between categorical variables.

Answer: Chi-square test of independence. Determines if two categorical variables are independent.

Flashcard 41: What is a 'confidence interval'?

Answer: Range of values likely to contain a population parameter. Provides an estimate with associated uncertainty.

Flashcard 42: What is the purpose of random assignment in experiments?

Answer: To eliminate bias by evenly distributing confounding variables. Ensures treatment and control groups are comparable on average.

Flashcard 43: Name the test for examining relationships between categorical variables.

Answer: Chi-square test of independence. Determines if two categorical variables are independent.

Flashcard 44: Find the critical value for a 95% confidence level (two-tailed).

Answer: $z^*$ = 1.96. Standard normal value capturing 95% of the distribution.

Flashcard 45: What is the purpose of replication in experiments?

Answer: To confirm results are consistent and not due to random chance. Increases confidence in findings through repeated validation.

Flashcard 46: Calculate the margin of error: $SE = 2.5$, $z^* = 1.96$.

Answer: 4.9. Margin of error = $SE \times z^* = 2.5 \times 1.96$.

Flashcard 47: What is the purpose of random assignment in experiments?

Answer: To eliminate bias by evenly distributing confounding variables. Ensures treatment and control groups are comparable on average.

Flashcard 48: Which design reduces variability by pairing similar subjects?

Answer: Matched pairs design. Effective method for controlling individual differences.

Flashcard 49: What does 'blocking' refer to in experiments?

Answer: Grouping similar experimental units to reduce variability. Improves precision by controlling for known sources of variation.

Flashcard 50: What is a 'p-value'?

Answer: Probability of observing data at least as extreme under $H_0$. Measures evidence against the null hypothesis.

Flashcard 51: What is a Type II error?

Answer: Failing to reject a false null hypothesis. A false negative error with probability $\beta$.

Flashcard 52: Identify the null hypothesis symbol.

Answer: $H_0$. Standard notation for the null hypothesis in statistics.

Flashcard 53: Identify the non-parametric alternative to the $t$-test.

Answer: Wilcoxon signed-rank test. Does not assume normal distribution of data.

Flashcard 54: What does 'ANOVA' stand for?

Answer: Analysis of Variance. Statistical method comparing means across multiple groups.

Flashcard 55: What is the 'law of large numbers'?

Answer: As sample size increases, sample mean approaches population mean. Foundation for probability and statistical inference.

Flashcard 56: What is the primary goal of randomization?

Answer: To reduce bias and confounding in the experiment. Creates comparable groups and eliminates systematic differences.

Flashcard 57: Define 'systematic sampling'.

Answer: Selecting every nth member from a list after a random start. Simple method but may introduce patterns or bias.

Flashcard 58: What does 'internal validity' refer to?

Answer: Extent to which cause-and-effect conclusions are warranted. Focuses on the accuracy of causal inferences.

Flashcard 59: What is the effect of increasing sample size on margin of error?

Answer: Decreases the margin of error. Larger samples provide more precise estimates.

Flashcard 60: What is a 'double-blind' experiment?

Answer: Neither participants nor researchers know who receives treatment. Prevents bias from expectations affecting results.

Flashcard 61: What is 'confounding'?

Answer: Distortion of the effect of one variable due to another. Makes it difficult to isolate the true effect.

Flashcard 62: What does 'random sampling' ensure?

Answer: Each member of the population has an equal chance of selection. Eliminates selection bias and enables valid inference.

Flashcard 63: What does 'statistical significance' mean?

Answer: A result unlikely to occur by chance alone, below a threshold $p$-value. Indicates the result is not likely due to random variation.

Flashcard 64: What is 'stratified sampling'?

Answer: Dividing population into subgroups and sampling each proportionally. Ensures all subgroups are adequately represented.

Flashcard 65: Calculate the margin of error: $SE = 2.5$, $z^* = 1.96$.

Answer: 4.9. Margin of error = $SE \times z^* = 2.5 \times 1.96$.

Flashcard 66: What is a Type I error?

Answer: Rejecting a true null hypothesis. A false positive error with probability $\alpha$.

Flashcard 67: Identify the alternative hypothesis symbol.

Answer: $H_a$. Standard notation for the alternative hypothesis in statistics.

Flashcard 68: Define 'standard deviation'.

Answer: Measure of data dispersion around the mean. Quantifies how spread out data points are.

Flashcard 69: What is the purpose of a placebo?

Answer: To account for the placebo effect in experiments. Controls for psychological effects of receiving treatment.

Flashcard 70: Identify the non-parametric alternative to the $t$-test.

Answer: Wilcoxon signed-rank test. Does not assume normal distribution of data.

Flashcard 71: Find the critical value for a 95% confidence level (two-tailed).

Answer: $z^*$ = 1.96. Standard normal value capturing 95% of the distribution.

Flashcard 72: Define 'power of a test'.

Answer: Probability of correctly rejecting a false null hypothesis. Power equals $1 - \beta$ where $\beta$ is Type II error rate.

Flashcard 73: Which test compares proportions?

Answer: Chi-square test. Tests independence or goodness of fit for categorical data.

Flashcard 74: What is the purpose of replication in experiments?

Answer: To confirm results are consistent and not due to random chance. Increases confidence in findings through repeated validation.

Flashcard 75: What does 'blocking' refer to in experiments?

Answer: Grouping similar experimental units to reduce variability. Improves precision by controlling for known sources of variation.

Flashcard 76: What is a 'double-blind' experiment?

Answer: Neither participants nor researchers know who receives treatment. Prevents bias from expectations affecting results.

Flashcard 77: State one advantage of stratified sampling.

Answer: Ensures representation of all subgroups in the sample. Particularly useful when subgroups differ significantly.

Flashcard 78: What does 'ANOVA' stand for?

Answer: Analysis of Variance. Statistical method comparing means across multiple groups.