AP Statistics Flashcards: Introducing Statistics Are My Results Unexpected

What this deck covers

This deck focuses on Introducing Statistics Are My Results Unexpected, 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 type of variable is height?

Answer: Quantitative variable. Numerical measurements that can be meaningfully ordered.

Flashcard 2: Identify the degrees of freedom in a t-test.

Answer: $n - 1$. Reflects loss of information from estimating population SD.

Flashcard 3: Find the critical z-value for a 95% confidence level.

Answer: $1.96$. Corresponds to 2.5% in each tail of standard normal.

Flashcard 4: Find the sample mean of the dataset: $5, 10, 15$.

Answer: $\bar{x} = 10$. $(5+10+15)/3 = 30/3 = 10$.

Flashcard 5: What is a two-tailed test?

Answer: A test where effects in both directions are considered. Alternative hypothesis allows for effects in either direction.

Flashcard 6: What is the purpose of a paired t-test?

Answer: To compare means from the same group at different times. Controls for individual differences by using matched pairs.

Flashcard 7: What is an outlier in a dataset?

Answer: A data point that differs significantly from other observations. Unusual values that don't fit the general pattern.

Flashcard 8: Find the sample mean of the dataset: $5, 10, 15$.

Answer: $\bar{x} = 10$. $(5+10+15)/3 = 30/3 = 10$.

Flashcard 9: What is the formula for the confidence interval for a population mean?

Answer: $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$. Uses critical value and standard error of the mean.

Flashcard 10: Find the z-score for $x = 10$, $\mu = 8$, $\sigma = 2$.

Answer: $z = 1$. $(10-8)/2 = 1$ standard deviation above mean.

Flashcard 11: What is the purpose of a paired t-test?

Answer: To compare means from the same group at different times. Controls for individual differences by using matched pairs.

Flashcard 12: What is the null hypothesis in an ANOVA test?

Answer: All group means are equal. ANOVA tests if all population means are identical.

Flashcard 13: Find the critical z-value for a 95% confidence level.

Answer: $1.96$. Corresponds to 2.5% in each tail of standard normal.

Flashcard 14: What does a high F-statistic in ANOVA indicate?

Answer: At least one group mean is different. Large F suggests between-group variation exceeds within-group.

Flashcard 15: What does it mean if a p-value is less than $\alpha$?

Answer: Reject the null hypothesis. Evidence is strong enough to conclude $H_a$ is true.

Flashcard 16: What is the formula for variance?

Answer: $\sigma^2$ or $s^2$. Variance equals standard deviation squared.

Flashcard 17: What does it mean if a p-value is less than $\alpha$?

Answer: Reject the null hypothesis. Evidence is strong enough to conclude $H_a$ is true.

Flashcard 18: What does a z-score indicate?

Answer: How many standard deviations an element is from the mean. It standardizes position relative to the distribution.

Flashcard 19: What is the null hypothesis in an ANOVA test?

Answer: All group means are equal. ANOVA tests if all population means are identical.

Flashcard 20: Identify the standard normal distribution.

Answer: Mean $0$, standard deviation $1$. The reference distribution for z-scores.

Flashcard 21: What is the formula for variance?

Answer: $\sigma^2$ or $s^2$. Variance equals standard deviation squared.

Flashcard 22: What type of variable is gender?

Answer: Categorical variable. Qualities or labels that classify observations.

Flashcard 23: Which error occurs if the null hypothesis is incorrectly accepted?

Answer: Type II error. False negative: failing to reject a false null hypothesis.

Flashcard 24: What is the purpose of a hypothesis test?

Answer: To determine if there is enough evidence to reject the null hypothesis. Provides systematic framework for decision-making with data.

Flashcard 25: Identify the symbol for the population mean.

Answer: $\mu$. Greek letter mu represents the true population average.

Flashcard 26: What does it mean if a result is statistically significant?

Answer: The result is unlikely due to chance, given $\alpha$. The observed difference is unlikely to be due to chance.

Flashcard 27: Identify the symbol for the sample standard deviation.

Answer: $s$. Lowercase s measures sample spread.

Flashcard 28: What is an outlier in a dataset?

Answer: A data point that differs significantly from other observations. Unusual values that don't fit the general pattern.

Flashcard 29: State the formula for calculating a z-score.

Answer: $z = \frac{x - \mu}{\sigma}$. Standardizes values by subtracting mean and dividing by SD.

Flashcard 30: What is the significance level commonly denoted as?

Answer: $\alpha$. Greek letter alpha sets our threshold for significance.

Flashcard 31: What is a one-tailed test?

Answer: A test where effects in only one direction are considered. Alternative hypothesis specifies direction of the effect.

Flashcard 32: Identify the symbol for the population mean.

Answer: $\mu$. Greek letter mu represents the true population average.

Flashcard 33: Which statistical test is used for comparing means of more than two groups?

Answer: ANOVA. Analysis of variance extends t-tests to multiple groups.

Flashcard 34: What does a p-value of 0.03 indicate at $\alpha = 0.05$?

Answer: Reject the null hypothesis. P-value is less than significance level.

Flashcard 35: What does it mean if a result is statistically significant?

Answer: The result is unlikely due to chance, given $\alpha$. The observed difference is unlikely to be due to chance.

Flashcard 36: What is the power of a test?

Answer: The probability of correctly rejecting a false null hypothesis. Higher power means better ability to detect real effects.

Flashcard 37: What is the typical significance level used in hypothesis testing?

Answer: $0.05$. This is the standard cutoff for statistical significance.

Flashcard 38: What is a one-tailed test?

Answer: A test where effects in only one direction are considered. Alternative hypothesis specifies direction of the effect.

Flashcard 39: Identify the symbol for the sample mean.

Answer: $\bar{x}$. X-bar represents the calculated average from sample data.

Flashcard 40: Find the z-score for $x = 10$, $\mu = 8$, $\sigma = 2$.

Answer: $z = 1$. $(10-8)/2 = 1$ standard deviation above mean.

Flashcard 41: What is the alternative hypothesis in hypothesis testing?

Answer: The alternative hypothesis states there is an effect or difference. It's what we're trying to prove or find evidence for.

Flashcard 42: Which error occurs if the null hypothesis is incorrectly accepted?

Answer: Type II error. False negative: failing to reject a false null hypothesis.

Flashcard 43: State the formula for calculating a z-score.

Answer: $z = \frac{x - \mu}{\sigma}$. Standardizes values by subtracting mean and dividing by SD.

Flashcard 44: Identify the degrees of freedom in a t-test.

Answer: $n - 1$. Reflects loss of information from estimating population SD.

Flashcard 45: What does a 95% confidence interval mean?

Answer: 95% of intervals will contain the true population parameter. It's about the method's long-run capture rate.

Flashcard 46: Which error occurs if the null hypothesis is incorrectly rejected?

Answer: Type I error. False positive: rejecting a true null hypothesis.

Flashcard 47: What does a p-value represent in hypothesis testing?

Answer: The probability of observing data at least as extreme assuming the null hypothesis is true. It measures how unusual our data would be under $H_0$.

Flashcard 48: What type of variable is height?

Answer: Quantitative variable. Numerical measurements that can be meaningfully ordered.

Flashcard 49: What is the formula for calculating a sample size for a given margin of error?

Answer: $n = \left(\frac{z^* \sigma}{E}\right)^2$. Balances desired precision with critical value and variability.

Flashcard 50: Which statistical test is used for comparing means of more than two groups?

Answer: ANOVA. Analysis of variance extends t-tests to multiple groups.

Flashcard 51: What is the null hypothesis in hypothesis testing?

Answer: The null hypothesis states there is no effect or difference. It's the baseline assumption we test against.

Flashcard 52: What does a p-value represent in hypothesis testing?

Answer: The probability of observing data at least as extreme assuming the null hypothesis is true. It measures how unusual our data would be under $H_0$.

Flashcard 53: Identify the symbol for standard deviation.

Answer: $\sigma$. Greek letter sigma measures population spread.

Flashcard 54: What is the chi-square test used for?

Answer: Testing independence or goodness of fit. Compares observed and expected frequencies in categories.

Flashcard 55: What does a z-score indicate?

Answer: How many standard deviations an element is from the mean. It standardizes position relative to the distribution.

Flashcard 56: What does a high F-statistic in ANOVA indicate?

Answer: At least one group mean is different. Large F suggests between-group variation exceeds within-group.

Flashcard 57: What is the significance level commonly denoted as?

Answer: $\alpha$. Greek letter alpha sets our threshold for significance.

Flashcard 58: What is the assumption for a t-test?

Answer: Data are normally distributed. Required for t-distribution to be appropriate.

Flashcard 59: What is the alternative hypothesis in hypothesis testing?

Answer: The alternative hypothesis states there is an effect or difference. It's what we're trying to prove or find evidence for.

Flashcard 60: What is the null hypothesis in hypothesis testing?

Answer: The null hypothesis states there is no effect or difference. It's the baseline assumption we test against.

Flashcard 61: Identify the symbol for the sample mean.

Answer: $\bar{x}$. X-bar represents the calculated average from sample data.

Flashcard 62: What is a two-tailed test?

Answer: A test where effects in both directions are considered. Alternative hypothesis allows for effects in either direction.

Flashcard 63: Which error occurs if the null hypothesis is incorrectly rejected?

Answer: Type I error. False positive: rejecting a true null hypothesis.

Flashcard 64: What is the formula for calculating a sample size for a given margin of error?

Answer: $n = \left(\frac{z^* \sigma}{E}\right)^2$. Balances desired precision with critical value and variability.

Flashcard 65: Identify the symbol for the sample standard deviation.

Answer: $s$. Lowercase s measures sample spread.

Flashcard 66: What type of variable is gender?

Answer: Categorical variable. Qualities or labels that classify observations.

Flashcard 67: Identify the standard normal distribution.

Answer: Mean $0$, standard deviation $1$. The reference distribution for z-scores.

Flashcard 68: What is the formula for a test statistic in a t-test?

Answer: $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$. Uses sample SD when population SD is unknown.

Flashcard 69: What is the formula for the confidence interval for a population mean?

Answer: $\bar{x} \pm z^* \frac{\sigma}{\sqrt{n}}$. Uses critical value and standard error of the mean.

Flashcard 70: What is the typical significance level used in hypothesis testing?

Answer: $0.05$. This is the standard cutoff for statistical significance.

Flashcard 71: What does a p-value of 0.03 indicate at $\alpha = 0.05$?

Answer: Reject the null hypothesis. P-value is less than significance level.

Flashcard 72: What is the formula for a test statistic in a t-test?

Answer: $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$. Uses sample SD when population SD is unknown.

Flashcard 73: Identify the symbol for standard deviation.

Answer: $\sigma$. Greek letter sigma measures population spread.

Flashcard 74: What is the assumption for a t-test?

Answer: Data are normally distributed. Required for t-distribution to be appropriate.

Flashcard 75: What is the power of a test?

Answer: The probability of correctly rejecting a false null hypothesis. Higher power means better ability to detect real effects.