AP Statistics Flashcards: Selecting Implementing And Communicating Inference Procedures

What this deck covers

This deck focuses on Selecting Implementing And Communicating Inference Procedures, 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: Identify the degrees of freedom for the numerator in an ANOVA test.

Answer: $k - 1$. Where $k$ is number of groups compared.

Flashcard 2: Identify the critical value for a 95% confidence interval using a z-distribution.

Answer: 1.96. Captures 95% of area under standard normal curve.

Flashcard 3: What does a significant F-statistic in ANOVA indicate?

Answer: At least one group mean is different. Not all group means are equal.

Flashcard 4: Identify the type of error when $H_0$ is true, but rejected.

Answer: Type I error. Rejecting true null hypothesis incorrectly.

Flashcard 5: Determine the p-value given a z-score of 1.96 in a two-tailed test.

Answer: 0.05. Two-tailed area beyond $z = 1.96$ is 0.05.

Flashcard 6: Identify the test for comparing paired sample means.

Answer: Paired t-test. Compares before and after measurements on same subjects.

Flashcard 7: Which test checks for independence between two categorical variables?

Answer: Chi-square test of independence. Tests if two categorical variables are related.

Flashcard 8: Which test is used when comparing the variance of a sample to a known variance?

Answer: Chi-square test. Compares sample variance to known population variance.

Flashcard 9: Which condition is checked for normality in a t-test?

Answer: The sample data is approximately normally distributed. Required for valid t-test inference procedures.

Flashcard 10: What is the alternative hypothesis for a two-tailed test?

Answer: $H_a: \text{parameter} \neq \text{value}$. Parameter differs from specified value in either direction.

Flashcard 11: State the null hypothesis for a test of a single proportion.

Answer: $H_0: p = p_0$. Tests if population proportion equals specific value.

Flashcard 12: Choose the correct decision rule: reject $H_0$ if p-value < $α$.

Answer: Correct. Standard decision rule for hypothesis testing.

Flashcard 13: What assumption is made about variances in ANOVA?

Answer: Homogeneity of variances. Equal variances across all groups required.

Flashcard 14: State the null hypothesis for an ANOVA test.

Answer: $H_0: \text{All group means are equal}$. No difference among any group means.

Flashcard 15: Identify the correct interpretation of a 95% confidence interval for a mean.

Answer: 95% of such intervals contain the true population mean. Describes long-run capture rate behavior.

Flashcard 16: Identify the critical value for a 95% confidence interval using a z-distribution.

Answer: 1.96. Captures 95% of area under standard normal curve.

Flashcard 17: Which test would you use for homogeneity of variance among groups?

Answer: Levene's test. Tests equal variances assumption for ANOVA.

Flashcard 18: What is the purpose of a confidence interval?

Answer: Estimate a population parameter with an associated level of confidence. Provides range of plausible parameter values.

Flashcard 19: Choose the correct decision rule: reject $H_0$ if p-value < $\alpha$.

Answer: Correct. Standard decision rule for hypothesis testing.

Flashcard 20: Which inference method is used when population variance is unknown?

Answer: T-distribution. Used when population standard deviation unknown.

Flashcard 21: Identify the degrees of freedom for the numerator in an ANOVA test.

Answer: $k - 1$. Where $k$ is number of groups compared.

Flashcard 22: Identify the alternative hypothesis for a left-tailed test.

Answer: $H_a: \text{parameter} < \text{value}$. Parameter is less than specified value.

Flashcard 23: What is the formula for the test statistic in a one-sample t-test?

Answer: $t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$. Standardizes sample mean using sample standard deviation.

Flashcard 24: Find the critical value for a 99% confidence interval using a t-distribution with 10 df.

Answer: 3.169. Critical value for 99% confidence with 10 degrees freedom.

Flashcard 25: What is the null hypothesis for a two-sample t-test?

Answer: $H_0: \text{The two population means are equal}$. States no difference between population means.

Flashcard 26: What is the null hypothesis for a two-sample t-test?

Answer: $H_0: \text{The two population means are equal}$. States no difference between population means.

Flashcard 27: Identify the type of error when $H_0$ is true, but rejected.

Answer: Type I error. Rejecting true null hypothesis incorrectly.

Flashcard 28: State the null hypothesis for a chi-square goodness-of-fit test.

Answer: $H_0: \text{The observed distribution fits the expected distribution}$. Tests if data follows expected distribution pattern.

Flashcard 29: Which option describes a Type II error?

Answer: Failing to reject $H_0$ when it is false. Accepting false null hypothesis incorrectly.

Flashcard 30: State the formula for the test statistic in a two-proportion z-test.

Answer: z = \frac{\text{p}_1 - \text{p}_2}{\text{√(p(1-p)(\frac{1}{n_1} + \frac{1}{n_2}))}}. Compares two population proportions using pooled estimate.

Flashcard 31: Which test statistic is used for proportions?

Answer: Z-test. Uses normal distribution for proportion tests.

Flashcard 32: Which test checks for independence between two categorical variables?

Answer: Chi-square test of independence. Tests if two categorical variables are related.

Flashcard 33: Identify the test for comparing paired sample means.

Answer: Paired t-test. Compares before and after measurements on same subjects.

Flashcard 34: What is the alternative hypothesis for a two-tailed test?

Answer: $H_a: \text{parameter} \neq \text{value}$. Parameter differs from specified value in either direction.

Flashcard 35: Which test would you use for homogeneity of variance among groups?

Answer: Levene's test. Tests equal variances assumption for ANOVA.

Flashcard 36: Find the critical value for a 99% confidence interval using a t-distribution with 10 df.

Answer: 3.169. Critical value for 99% confidence with 10 degrees freedom.

Flashcard 37: Identify the degrees of freedom for the denominator in an ANOVA test.

Answer: $N - k$. Where $N$ is total sample size, $k$ is groups.

Flashcard 38: Identify the condition for sample proportions in hypothesis testing.

Answer: np ≥ 10 and n(1-p) ≥ 10. Ensures normal approximation validity for proportions.

Flashcard 39: What is the formula for the standard error of a sample mean?

Answer: $SE = \frac{s}{\sqrt{n}}$. Measures variability of sample mean estimates.

Flashcard 40: Determine the p-value given a z-score of 1.96 in a two-tailed test.

Answer: 0.05. Two-tailed area beyond $z = 1.96$ is 0.05.

Flashcard 41: Which test is used when comparing the variance of a sample to a known variance?

Answer: Chi-square test. Compares sample variance to known population variance.

Flashcard 42: What is the formula for the chi-square statistic?

Answer: $χ^2 = \text{Σ} \frac{(O_i - E_i)^2}{E_i}$. Compares observed frequencies to expected frequencies.

Flashcard 43: Which condition is checked for normality in a t-test?

Answer: The sample data is approximately normally distributed. Required for valid t-test inference procedures.

Flashcard 44: State the null hypothesis for a test of a single proportion.

Answer: $H_0: p = p_0$. Tests if population proportion equals specific value.

Flashcard 45: State the null hypothesis for an ANOVA test.

Answer: $H_0: \text{All group means are equal}$. No difference among any group means.

Flashcard 46: State the null hypothesis for a chi-square goodness-of-fit test.

Answer: $H_0: \text{The observed distribution fits the expected distribution}$. Tests if data follows expected distribution pattern.

Flashcard 47: What assumption is made about variances in ANOVA?

Answer: Homogeneity of variances. Equal variances across all groups required.

Flashcard 48: What does a significant F-statistic in ANOVA indicate?

Answer: At least one group mean is different. Not all group means are equal.

Flashcard 49: Which test statistic is used for proportions?

Answer: Z-test. Uses normal distribution for proportion tests.

Flashcard 50: Identify the correct interpretation of a 95% confidence interval for a mean.

Answer: 95% of such intervals contain the true population mean. Describes long-run capture rate behavior.

Flashcard 51: What is the purpose of a confidence interval?

Answer: Estimate a population parameter with an associated level of confidence. Provides range of plausible parameter values.

Flashcard 52: What is the formula for the test statistic in a one-sample t-test?

Answer: $t = \frac{\bar{x} - \mu}{s / \sqrt{n}}$. Standardizes sample mean using sample standard deviation.

Flashcard 53: Which inference method is used when population variance is unknown?

Answer: T-distribution. Used when population standard deviation unknown.

Flashcard 54: Identify the degrees of freedom for the denominator in an ANOVA test.

Answer: $N - k$. Where $N$ is total sample size, $k$ is groups.

Flashcard 55: What is the formula for the standard error of a sample mean?

Answer: $SE = \frac{s}{\sqrt{n}}$. Measures variability of sample mean estimates.

Flashcard 56: State the formula for the test statistic in a two-proportion z-test.

Answer: z = \frac{\text{p}_1 - \text{p}_2}{\text{√(p(1-p)(\frac{1}{n_1} + \frac{1}{n_2}))}}. Compares two population proportions using pooled estimate.

Flashcard 57: Identify the alternative hypothesis for a left-tailed test.

Answer: $H_a: \text{parameter} < \text{value}$. Parameter is less than specified value.

Flashcard 58: What is the test statistic formula for an ANOVA test?

Answer: $F = \frac{\text{MSB}}{\text{MSW}}$. Ratio of between-group to within-group variance.

Flashcard 59: Which test would you use for comparing means of two independent samples?

Answer: Two-sample t-test. Compares means when groups are independent.

Flashcard 60: What is the p-value interpretation in hypothesis testing?

Answer: Probability of observing data as extreme as current, under $H_0$. Measures strength of evidence against null hypothesis.

Flashcard 61: What is the test statistic formula for an ANOVA test?

Answer: $F = \frac{\text{MSB}}{\text{MSW}}$. Ratio of between-group to within-group variance.

Flashcard 62: Choose the formula for calculating a confidence interval for a mean.

Answer: $\bar{x} \pm t \frac{s}{\sqrt{n}}$. Uses t-distribution critical value for unknown variance.

Flashcard 63: Choose the formula for calculating a confidence interval for a mean.

Answer: $\bar{x} \pm t* \frac{s}{\sqrt{n}}$. Uses t-distribution critical value for unknown variance.

Flashcard 64: What is the significance level commonly denoted as?

Answer: $\text{α}$. Probability of Type I error threshold.

Flashcard 65: What is the formula for the margin of error in a confidence interval?

Answer: $\text{ME} = z* \frac{σ}{\sqrt{n}}$. Half-width of confidence interval around estimate.

Flashcard 66: What is the p-value interpretation in hypothesis testing?

Answer: Probability of observing data as extreme as current, under $H_0$. Measures strength of evidence against null hypothesis.

Flashcard 67: Which test would you use for comparing means of two independent samples?

Answer: Two-sample t-test. Compares means when groups are independent.