Enduring Understanding	Learning Objective	Essential Knowledge
UNC-4 An interval of values should be used to estimate parameters, in order to account for uncertainty.	UNC-4.A Identify an appropriate confidence interval procedure for a population proportion. [Skill 1.D]	UNC-4.A.1 The appropriate confidence interval procedure for a one-sample proportion for one categorical variable is a one sample $z$-interval for a proportion.
	UNC-4.B Verify the conditions for calculating confidence intervals for a population proportion. [Skill 4.C]	UNC-4.B.1 In order to make assumptions necessary for inference on population proportions, means, and slopes, we must check for independence in data collection methods and for selection of the appropriate sampling distribution. UNC-4.B.2 In order to calculate a confidence interval to estimate a population proportion, $p$, we must check for independence and that the sampling distribution is approximately normal. a. To check for independence: i. Data should be collected using a random sample or a randomized experiment. ii. When sampling without replacement, check that $n \leq 10\%N$, where $N$ is the size of the population. b. To check that the sampling distribution of $\hat{p}$ is approximately normal (shape): i. For categorical variables, check that both the number of successes, $n\hat{p}$, and the number of failures, $n(1-\hat{p})$ are at least 10 so that the sample size is large enough to support an assumption of normality.
	UNC-4.C Determine the margin of error for a given sample size and an estimate for the sample size that will result in a given margin of error for a population proportion. [Skill 3.D]	UNC-4.C.1 Based on sample data, the standard error of a statistic is an estimate for the standard deviation for the statistic. The standard error of $\hat{p}$ is $SE_{\hat{p}} = \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$. UNC-4.C.2 A margin of error gives how much a value of a sample statistic is likely to vary from the value of the corresponding population parameter. UNC-4.C.3 For categorical variables, the margin of error is the critical value ($z^$) times the standard error (SE) of the relevant statistic, which equals $z^ \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$ for a one sample proportion. UNC-4.C.4 The formula for margin of error can be rearranged to solve for $n$, the minimum sample size needed to achieve a given margin of error. For this purpose, use a guess for $\hat{p}$ or use $\hat{p} = 0.5$ in order to find an upper bound for the sample size that will result in a given margin of error.
	UNC-4.D Calculate an appropriate confidence interval for a population proportion. [Skill 3.D]	UNC-4.D.1 In general, an interval estimate can be constructed as point estimate ± (margin of error). For a one-sample proportion, the interval estimate is $\hat{p} \pm z^* \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$. Clarifying statement: Formulas for interval estimates do not appear explicitly on the AP Statistics Formula Sheet provided with the AP Statistics Exam. However, these formulas do not need to be memorized, as they can be constructed based on the general test statistic formula and the relevant standard error formulas that are provided on the formula sheet. UNC-4.D.2 Critical values represent the boundaries encompassing the middle C% of the standard normal distribution, where C% is an approximate confidence level for a proportion.
	UNC-4.E Calculate an interval estimate based on a confidence interval for a population proportion. [Skill 3.D]	UNC-4.E.1 Confidence intervals for population proportions can be used to calculate interval estimates with specified units.

English	Tiếng Việt
inference/ˈɪnfərəns/	suy luận
confidence interval/ˈkɒnfɪdəns ˈɪntəvl/	khoảng tin cậy
margin of error/ˈmɑːdʒɪn ɒv ˈerə/	biên độ sai số
confidence level/ˈkɒnfɪdəns ˈlevl/	mức độ tin cậy
significance test/sɪɡˈnɪfɪkəns test/	kiểm định ý nghĩa
null hypothesis/nʌl haɪˈpɒθəsɪs/	giả thuyết không
alternative hypothesis/ɔːlˈtɜːnətɪv haɪˈpɒθəsɪs/	giả thuyết thay thế
test statistic/test stəˈtɪstɪk/	thống kê kiểm định
significance level/sɪɡˈnɪfɪkəns ˈlevl/	mức ý nghĩa
Type I error/taɪp aɪ ˈerə/	lỗi loại I
Type II error/taɪp ˈtuː ˈerə/	lỗi loại II
power/ˈpaʊə/	công suất
combined (pooled)/kəmˈbaɪnd/	tổ hợp (gộp)

Enduring Understanding	Learning Objective	Essential Knowledge
VAR-6 The normal distribution may be used to model variation.	VAR-6.D Identify the null and alternative hypotheses for a population proportion. [Skill 1.F]	VAR-6.D.1 The null hypothesis is the situation that is assumed to be correct unless evidence suggests otherwise, and the alternative hypothesis is the situation for which evidence is being collected. VAR-6.D.2 For hypotheses about parameters, the null hypothesis contains an equality reference (=, ≥, or ≤), while the alternative hypothesis contains a strict inequality (<, >, or ≠). The type of inequality in the alternative hypothesis is based on the question of interest. Alternative hypotheses with < or > are called one-sided, and alternative hypotheses with ≠ are called two-sided. Although the null hypothesis for a one-sided test may include an inequality symbol, it is still tested at the boundary of equality. VAR-6.D.3 The null hypothesis for a population proportion is: $H_0 : p = p_0$, where $p_0$ is the null hypothesized value for the population proportion. VAR-6.D.4 A one-sided alternative hypothesis for a proportion is either $H_a : p < p_0$ or $H_a : p > p_0$. A two-sided alternate hypothesis is $H_a : p_1 \neq p_2$. VAR-6.D.5 For a one-sample $z$-test for a population proportion, the null hypothesis specifies a value for the population proportion, usually one indicating no difference or effect.
	VAR-6.E Identify an appropriate testing method for a population proportion. [Skill 1.E]	VAR-6.E.1 For a single categorical variable, the appropriate testing method for a population proportion is a one-sample $z$-test for a population proportion.
	VAR-6.F Verify the conditions for making statistical inferences when testing a population proportion. [Skill 4.C]	VAR-6.F.1 In order to make statistical inferences when testing a population proportion, we must check for independence and that the sampling distribution is approximately normal: a. To check for independence: i. Data should be collected using a random sample or a randomized experiment. ii. When sampling without replacement, check that $n \leq 10\%N$. b. To check that the sampling distribution of $\hat{p}$ is approximately normal (shape): i. Assuming that $H_0$ is true $(p = p_0)$, verify that both the number of successes, $np_0$, and the number of failures, $n(1-p_0)$ are at least 10 so that that the sample size is large enough to support an assumption of normality.

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