Key Concept Questions: AP Statistics

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📘 Key Concept Questions: AP Statistics

What is the Central Limit Theorem (CLT)? (*****)

What is a confidence interval? (*****)

What is a hypothesis test?

What is a P-value? (*****)

What is a Type I error in hypothesis testing?

What is a Type II error in hypothesis testing? (*****)

What does it mean if the P-value is small (e.g., < 0.05)?

What does a 95% confidence level mean?

What is the standard error of a sample mean?

What is the null hypothesis?

What is the alternative hypothesis?

What does "statistically significant" mean?

What conditions must be met to use a one-sample z-test for proportions?

What is the purpose of a chi-square test? (*****)

When do you use a t-distribution instead of a z-distribution?

What is the margin of error?

What is a sampling distribution?

What are the conditions for the Central Limit Theorem to apply?

What does it mean when two events are independent? (*****)

What is the formula for a confidence interval for a proportion?

Detailed answers：

📘 AP Statistics Key Concept Questions + Detailed Answers

No.	Question	Detailed Answer
1	What is the Central Limit Theorem (CLT)?	The CLT states that the sampling distribution of the sample mean will be approximately normal if the sample size is large enough (usually n≥30n ≥ 30), regardless of the population's distribution.
2	What is a confidence interval?	A range of values, based on sample data, that is likely to contain the true population parameter. It is calculated as: statistic ± margin of error.
3	What is a hypothesis test?	A method of using sample data to evaluate a claim (hypothesis) about a population. It involves a null and an alternative hypothesis.
4	What is a P-value?	The probability of observing a sample statistic as extreme as the one obtained, assuming the null hypothesis is true. A small P-value suggests strong evidence against the null.
5	What is a Type I error?	Rejecting the null hypothesis when it is actually true (false positive). Its probability is denoted by α\alpha.
6	What is a Type II error?	Failing to reject the null hypothesis when it is false (false negative). Its probability is denoted by β\beta.
7	What does it mean if the P-value is small?	It indicates strong evidence against the null hypothesis. If the P-value < α\alpha, you reject the null.
8	What does a 95% confidence level mean?	If you repeated the sampling process many times, about 95% of the resulting confidence intervals would contain the true population parameter.
9	What is the standard error of a sample mean?	It estimates the variability of the sample mean and is calculated as σn\frac{\sigma}{\sqrt{n}} (or sn\frac{s}{\sqrt{n}} if population SD is unknown).
10	What is the null hypothesis?	A claim about the population that we test against. Usually states “no effect” or “no difference” (e.g., H0:p=0.5H_0: p = 0.5).
11	What is the alternative hypothesis?	A claim we want to find evidence for. It represents an effect, difference, or change (e.g., HA:p>0.5H_A: p > 0.5).
12	What does "statistically significant" mean?	A result is statistically significant if the P-value is smaller than the chosen significance level α\alpha; this suggests strong evidence against H0H_0.
13	What conditions must be met to use a one-sample z-test for proportions?	1) Random sample, 2) 10% condition (if sampling without replacement), 3) Large counts: np≥10np ≥ 10 and n(1−p)≥10n(1-p) ≥ 10.
14	What is the purpose of a chi-square test?	To test for differences in categorical data, such as independence of variables or whether distributions match expected counts.
15	When do you use a t-distribution instead of a z-distribution?	When the population standard deviation is unknown and the sample size is small (n<30n < 30), especially for inference about means.
16	What is the margin of error?	The maximum expected difference between the sample statistic and the true population parameter; calculated using a critical value times the standard error.
17	What is a sampling distribution?	The distribution of a statistic (e.g., sample mean or sample proportion) over all possible samples of a given size from a population.
18	What are the conditions for the Central Limit Theorem to apply?	The sample must be random and either: (1) the population is normal, or (2) the sample size is large (n≥30n ≥ 30).
19	What does it mean when two events are independent?	The occurrence of one event does not affect the probability of the other. Mathematically: P(A∩B)=P(A)P(B)P(A \cap B) = P(A)P(B).
20	What is the formula for a confidence interval for a proportion?	p^±z∗p^(1−p^)n\hat{p} \pm z^* \sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}, where p^\hat{p} is the sample proportion and z∗z^* is the critical value.

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