AP Statistics

Final Exam Review (Chapters 8 - 13)

Key Terms and Concepts

Statistic	Any quantity whose value is computed from sample data.
Sampling Distribution	The probability distribution of a statistic: The sampling distribution describes the long-run behavior of the statistic.
Sampling Distribution of	The probability distribution of the sample mean , based on a random sample of size n.  Properties of the sampling distribution: and (where and are the population mean and standard deviation, respectively). In addition, when the population distribution is normal or the sample size is large, the sampling distribution of is (approximately) normal.
Central Limit Theorem	This important theorem states that when n is sufficiently large, the distribution will be approximately normal. The standard rule of thumb is that the theorem can safely be applied when n exceeds 30.
Sampling distribution of p	The probability distribution of the sample proportion p, based on a random sample of size n. When the sample size is sufficiently large, the sampling distribution of p is approximately normal, with and (where is the true population proportion).
Point estimate	A single number, based on sample data, that represents a plausible value of a population characteristic.
Unbiased statistic	A statistic that has a sampling distribution with a mean equal to the value of the population characteristic to be estimated.
Confidence interval	An interval that is computed from sample data and provides a range of plausible values for a population characteristic.
Confidence level	A number that provides information on how much "confidence " we can have in the method used to construct a confidence interval estimate.   The confidence level specifies the percentage of all possible samples that will produce an interval containing the true value of the population characteristic.
	A formula used to construct a confidence interval for π when the sample size is large.
n = π(1 - π)	A formula used to compute the sample size necessary for estimating π to within an amount B with 95% confidence. (For other confidence levels, replace 1.96 with an appropriate z-critical value.)
x ± (z critical value)	A formula used to construct a confidence interval for μ  when σ is known and either the sample size is large or the population distribution is normal.
x ± (t critical value)	A formula used for constructing a confidence interval for μ when σ is unknown and either the sample size is large or the population distribution is normal.
	A formula used to compute the sample size necessary for estimating μ to within an amount B with 95% confidence. (For other confidence levels, replace 1.96 with an appropriate z critical value.)
Hypothesis	A claim about the value of a population characteristic.
Null Hypothesis, H0	The hypothesis initially assumed to be true. It has the form H0: population characteristic = hypothesized value.
Alternative Hypothesis, Ha	A hypothesis that specifies a claim that is contradictory to H0 and is judged the more plausible claim when H0 is rejected.
Type I Error	Rejection of H0 when H0 is true; the probability of a type I error is denoted by α and is usually referred to as the significance level for the test.
Type II Error	Non-rejection of H0 when H0 is false; the probability of a type II error is denoted by β.
Test Statistic	The quantity computed from sample data for making a decision between H0 and Ha.
P-value	The probability, computed assuming H0 to be true, of obtaining a value of the test statistic at least as contradictory to H0 as what actually resulted. H0 is rejected if P-value < α and not rejected if P-value > α, where α is the chosen significance level.
	A test statistic for testing H0: π = hypothesized value when the sample size is large. The P-value is determined from the z-curve.
	A test statistic for testing H0:  μ  = hypothesized value when σ is known and either the sample size is large or the population distribution is normal. The P-value is determined from the z-curve.
	A test statistic for testing H0: μ = hypothesized value when σ is unknown and either the sample size is large or the population distribution is normal. The P-value is determined from the t-curve with df = (n - 1).
Power	The power of a test is the probability of rejecting the null hypothesis. Power is affected by the size of the difference between the hypothesized value and the true value, the sample size, and the significance level.
Independent Samples	Two samples where the individuals or objects in the first sample are selected independently from those in the second sample.
Paired Samples	Two samples for which each observation in the first sample is paired in a meaningful way with a particular observation in the second sample.
	The test statistic for testing H0: μ1 μ2 = hypothesized value when the samples are independently selected and the sample sizes are large or it is reasonable to assume that both population distributions are normal.
(x1- x2) ± (t crit. value)	A formula for constructing a confidence interval for μ1 μ2 when the samples are independently selected and the sample sizes are large or it is reasonable to assume that both population distributions are normal.
	The formula for determining the df for the two-sample t test and confidence interval.
xd	The sample mean difference.
sd	The standard deviation of the sample differences.
μd	The mean value of the population of differences.
σd	The standard deviation for the population of differences.
	The paired t test statistic for testing H0: μd  =  hypothesized value.
(xd) ± (t critical value)	The paired t confidence interval formula.
Combined estimate of the common population proportion:	pc is the statistic for estimating the common population proportion when π1 = π2.
	The test statistic for testing H0: π1 - π2 = 0 when both sample sizes are large.
	A formula for constructing a confidence interval for π1 - π2 when both sample sizes are large.
One-way frequency table	A compact way of summarizing data on a categorical variable; it gives the number of times each of the possible categories in the data set occurs (the frequencies).
Goodness-of-fit statistic,	A statistic used to provide a comparison between observed counts and those expected when a given hypothesis is true. When none of the expected counts is too small, X2 has approximately a chi-squared distribution.
X2 test in a one-way frequency table:	A hypothesis test performed to determine whether the true category proportions are different from those specified by the given null hypothesis.
Two-way frequency table (contingency table)	A rectangular table used to summarize a bivariate categorical data set; two-way tables are used to compare several populations on the basis of a categorical variable or to identify whether an association exists between two categorical variables.
X2 test for comparing two or more populations: Ho: The true category proportions are the same for all of the populations.	The hypothesis test performed to determine whether the true category proportions are the same for all of the populations to be compared.
X2 test for independence: Ho: The two variables defining the table are independent	The hypothesis test performed to determine whether an association exists between two categorical variables.
Estimated regression line:	The least squares line introduced in Chapter 5
	The point estimate of the standard deviation, with associated degrees of freedom n-2.
	The estimated standard deviation of the statistic b.
	A confidence interval for the slope β of the population regression line, where the t critical value is based on (n-2) df.
	The test statistic for testing hypotheses about β. The test is based on n-2 df.

Notes from Mrs. Caso

Interactive Materials

Schedule

Timeline:	7 days
Day 172: 05/29/12	Review Chapters 8-9	Senior Exam Day 1
Day 173: 05/30/12	Review Chapters 9-10	Senior Exam Day 2
Day 174: 05/31/12	Review Chapters 10-11
Day 175: 06/01/12	Review Chapter 12-13
Day 176: 06/04/12	Exam Day 1: Periods 1, 2, & 3
Day 177: 06/05/12	Exam Day 2: Periods  4/5, 6/7, & 8/9
Day 178: 06/06/12	Exam Day 3: Periods 10 & 11