AP Statistics Flashcards: Interpreting P Values

What this deck covers

This deck focuses on Interpreting P Values, 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 on power when the significance level is increased?

Answer: Power increases. Higher $\alpha$ makes it easier to reject false $H_0$.

Flashcard 2: What does a p-value of 0.001 suggest about the null hypothesis?

Answer: Strong evidence to reject the null hypothesis. Very small p-value provides strong evidence against $H_0$.

Flashcard 3: What is considered a statistically significant p-value?

Answer: A p-value less than the significance level. When $p < \alpha$, results are statistically significant.

Flashcard 4: State the p-value threshold for a 5% significance level.

Answer: $0.05$. The cutoff value for determining statistical significance.

Flashcard 5: What does a small p-value indicate about the null hypothesis?

Answer: Evidence against the null hypothesis. Small p-values suggest data is unlikely under $H_0$.

Flashcard 6: What is the typical confidence level corresponding to a 5% significance level?

Answer: 95\text{%}. Standard confidence level when $\alpha = 0.05$.

Flashcard 7: What is the relationship between confidence level and Type I error?

Answer: Confidence level is $1 - \text{Type I error rate}$. Confidence level and Type I error rate are complements.

Flashcard 8: Identify the term for the probability of a Type II error.

Answer: Beta ($\beta$). The probability of incorrectly failing to reject $H_0$.

Flashcard 9: What does a large p-value indicate about the null hypothesis?

Answer: Insufficient evidence against the null hypothesis. Large p-values suggest data is consistent with $H_0$.

Flashcard 10: What is the complement of the significance level?

Answer: Confidence level. Confidence level $= 1 - \alpha$.

Flashcard 11: What type of error occurs when the null hypothesis is incorrectly rejected?

Answer: Type I error. Rejecting a true null hypothesis; probability equals $\alpha$.

Flashcard 12: What is the p-value if the test statistic equals the critical value?

Answer: Equal to the significance level. Critical value corresponds exactly to the significance level.

Flashcard 13: What does a p-value represent in hypothesis testing?

Answer: The probability of observing data as extreme as the sample, assuming the null hypothesis is true. It quantifies how unlikely the observed data would be under $H_0$.

Flashcard 14: Which hypothesis is tested against which in hypothesis testing?

Answer: Null hypothesis against the alternative hypothesis. The null is tested to see if alternative is supported.

Flashcard 15: What happens to the p-value if the test statistic increases?

Answer: The p-value decreases. Larger test statistics move further into rejection region.

Flashcard 16: What is the primary use of p-values in statistics?

Answer: To decide whether to reject the null hypothesis. P-values provide evidence for or against $H_0$.

Flashcard 17: Identify the term for the probability of a Type I error.

Answer: Significance level ($\text{alpha}$). The probability of incorrectly rejecting $H_0$.

Flashcard 18: What happens to the p-value if the test statistic increases?

Answer: The p-value decreases. Larger test statistics move further into rejection region.

Flashcard 19: What is the typical confidence level corresponding to a 5% significance level?

Answer: 95\text{%}. Standard confidence level when $\alpha = 0.05$.

Flashcard 20: What is the relationship between p-value and statistical significance?

Answer: Lower p-values indicate higher statistical significance. Smaller p-values indicate stronger evidence against $H_0$.

Flashcard 21: What is the relationship between confidence level and Type I error?

Answer: Confidence level is $1 - \text{Type I error rate}$. Confidence level and Type I error rate are complements.

Flashcard 22: What is the decision if p-value is 0.045 at a 5% significance level?

Answer: Reject the null hypothesis. Since $0.045 < 0.05$, evidence supports rejecting $H_0$.

Flashcard 23: What conclusion is drawn if the p-value is greater than the significance level?

Answer: Fail to reject the null hypothesis. When $p > \alpha$, insufficient evidence to reject $H_0$.

Flashcard 24: What does a large p-value indicate about the null hypothesis?

Answer: Insufficient evidence against the null hypothesis. Large p-values suggest data is consistent with $H_0$.

Flashcard 25: What is the relationship between p-value and test statistic?

Answer: The smaller the p-value, the larger the test statistic. Larger test statistics yield smaller p-values.

Flashcard 26: What type of error occurs when the null hypothesis is incorrectly not rejected?

Answer: Type II error. Failing to reject a false null hypothesis; probability equals $\beta$.

Flashcard 27: Which hypothesis is tested against which in hypothesis testing?

Answer: Null hypothesis against the alternative hypothesis. The null is tested to see if alternative is supported.

Flashcard 28: If p-value is 0.07 at a 5% significance level, what is the decision?

Answer: Fail to reject the null hypothesis. Since $0.07 > 0.05$, insufficient evidence against $H_0$.

Flashcard 29: What is the effect on power when the significance level is increased?

Answer: Power increases. Higher $\alpha$ makes it easier to reject false $H_0$.

Flashcard 30: What does a p-value of exactly 0.05 suggest at a 5% significance level?

Answer: Borderline decision; often interpreted as fail to reject. Exactly at threshold; convention varies by context.

Flashcard 31: What is the typical interpretation of a p-value close to 1?

Answer: Very weak evidence against the null hypothesis. P-values near 1 suggest data strongly supports $H_0$.

Flashcard 32: Identify the significance level commonly used in hypothesis testing.

Answer: $\text{0.05}$. Most commonly used threshold for statistical significance.

Flashcard 33: What does a two-tailed test examine regarding p-values?

Answer: Both ends of the distribution for extreme values. Tests for differences in either direction from $H_0$.

Flashcard 34: Which error increases when the significance level is reduced?

Answer: Type II error. Smaller $\alpha$ makes it harder to reject $H_0$.

Flashcard 35: What is the relationship between p-value and statistical significance?

Answer: Lower p-values indicate higher statistical significance. Smaller p-values indicate stronger evidence against $H_0$.

Flashcard 36: What is considered a statistically significant p-value?

Answer: A p-value less than the significance level. When $p < \alpha$, results are statistically significant.

Flashcard 37: What does a two-tailed test examine regarding p-values?

Answer: Both ends of the distribution for extreme values. Tests for differences in either direction from $H_0$.

Flashcard 38: What happens if the p-value is less than the significance level?

Answer: Reject the null hypothesis. When $p < \alpha$, evidence against $H_0$ is strong enough.

Flashcard 39: What is the inference when p-value equals significance level?

Answer: Test is inconclusive. Borderline case requires careful interpretation or more data.

Flashcard 40: Which hypothesis is assumed true when calculating the p-value?

Answer: Null hypothesis ($H_0$). P-values are calculated assuming $H_0$ is true.

Flashcard 41: What is the effect of a larger sample size on p-values?

Answer: P-values tend to decrease. Larger samples provide more precise evidence about $H_0$.

Flashcard 42: What is the term for the probability of correctly rejecting a false null hypothesis?

Answer: Power of the test. Power $= 1 - \beta$; probability of detecting false $H_0$.

Flashcard 43: Identify the term for the probability of a Type I error.

Answer: Significance level $\text{alpha}$. The probability of incorrectly rejecting $H_0$.

Flashcard 44: State the typical significance level for a stringent test.

Answer: $\text{0.01}$. Used when requiring stronger evidence against $H_0$.

Flashcard 45: What conclusion is drawn if the p-value is greater than the significance level?

Answer: Fail to reject the null hypothesis. When $p > \alpha$, insufficient evidence to reject $H_0$.

Flashcard 46: What is the inference when p-value equals significance level?

Answer: Test is inconclusive. Borderline case requires careful interpretation or more data.

Flashcard 47: What type of error occurs when the null hypothesis is incorrectly rejected?

Answer: Type I error. Rejecting a true null hypothesis; probability equals $\alpha$.

Flashcard 48: What does a p-value of 0.03 indicate at a 5% significance level?

Answer: Reject the null hypothesis. Since $0.03 < 0.05$, evidence supports rejecting $H_0$.

Flashcard 49: State the typical significance level for a stringent test.

Answer: $\text{0.01}$. Used when requiring stronger evidence against $H_0$.

Flashcard 50: What is the relationship between p-value and test statistic?

Answer: The smaller the p-value, the larger the test statistic. Larger test statistics yield smaller p-values.

Flashcard 51: What is the alternative hypothesis symbol in statistics?

Answer: $H_a$. Standard notation for the competing hypothesis.

Flashcard 52: What is the alternative hypothesis symbol in statistics?

Answer: $H_a$. Standard notation for the competing hypothesis.

Flashcard 53: What conclusion is drawn with a p-value of 0.20 at a 5% significance level?

Answer: Fail to reject the null hypothesis. Since $0.20 > 0.05$, insufficient evidence against $H_0$.

Flashcard 54: What does a p-value of 0.001 suggest about the null hypothesis?

Answer: Strong evidence to reject the null hypothesis. Very small p-value provides strong evidence against $H_0$.

Flashcard 55: What is the typical interpretation of a p-value close to 1?

Answer: Very weak evidence against the null hypothesis. P-values near 1 suggest data strongly supports $H_0$.

Flashcard 56: Which error increases when the significance level is reduced?

Answer: Type II error. Smaller $\alpha$ makes it harder to reject $H_0$.

Flashcard 57: Identify the significance level commonly used in hypothesis testing.

Answer: $\text{0.05}$. Most commonly used threshold for statistical significance.

Flashcard 58: What is the primary use of p-values in statistics?

Answer: To decide whether to reject the null hypothesis. P-values provide evidence for or against $H_0$.

Flashcard 59: What does a small p-value indicate about the null hypothesis?

Answer: Evidence against the null hypothesis. Small p-values suggest data is unlikely under $H_0$.

Flashcard 60: What is the decision if p-value is 0.045 at a 5% significance level?

Answer: Reject the null hypothesis. Since $0.045 < 0.05$, evidence supports rejecting $H_0$.

Flashcard 61: What happens if the p-value is less than the significance level?

Answer: Reject the null hypothesis. When $p < \alpha$, evidence against $H_0$ is strong enough.

Flashcard 62: What type of error occurs when the null hypothesis is incorrectly not rejected?

Answer: Type II error. Failing to reject a false null hypothesis; probability equals $\beta$.

Flashcard 63: If p-value is 0.07 at a 5% significance level, what is the decision?

Answer: Fail to reject the null hypothesis. Since $0.07 > 0.05$, insufficient evidence against $H_0$.

Flashcard 64: What does a p-value of exactly 0.05 suggest at a 5% significance level?

Answer: Borderline decision; often interpreted as fail to reject. Exactly at threshold; convention varies by context.

Flashcard 65: State the p-value threshold for a 5% significance level.

Answer: $0.05$. The cutoff value for determining statistical significance.

Flashcard 66: What is the null hypothesis symbol in statistics?

Answer: $H_0$. Standard notation for the hypothesis being tested.

Flashcard 67: Identify the term for the probability of a Type II error.

Answer: Beta ($\beta$). The probability of incorrectly failing to reject $H_0$.

Flashcard 68: How is the p-value related to the significance level in hypothesis testing?

Answer: It determines if the null hypothesis should be rejected. Compare p-value to $\alpha$ to make rejection decision.

Flashcard 69: What is the p-value if the test statistic equals the critical value?

Answer: Equal to the significance level. Critical value corresponds exactly to the significance level.

Flashcard 70: What does a p-value of 0.03 indicate at a 5% significance level?

Answer: Reject the null hypothesis. Since $0.03 < 0.05$, evidence supports rejecting $H_0$.

Flashcard 71: Which hypothesis is assumed true when calculating the p-value?

Answer: Null hypothesis ($H_0$). P-values are calculated assuming $H_0$ is true.

Flashcard 72: What is the effect of a larger sample size on p-values?

Answer: P-values tend to decrease. Larger samples provide more precise evidence about $H_0$.

Flashcard 73: What conclusion is drawn with a p-value of 0.20 at a 5% significance level?

Answer: Fail to reject the null hypothesis. Since $0.20 > 0.05$, insufficient evidence against $H_0$.

Flashcard 74: How is the p-value related to the significance level in hypothesis testing?

Answer: It determines if the null hypothesis should be rejected. Compare p-value to $\alpha$ to make rejection decision.

Flashcard 75: What is the complement of the significance level?

Answer: Confidence level. Confidence level $= 1 - \alpha$.

Flashcard 76: What is the term for the probability of correctly rejecting a false null hypothesis?

Answer: Power of the test. Power $= 1 - \beta$; probability of detecting false $H_0$.

Flashcard 77: What is the null hypothesis symbol in statistics?

Answer: $H_0$. Standard notation for the hypothesis being tested.