Mr. Rogers - AP Statistics Objectives

Syllabus	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
Chap 6 Probability	7&8 Binomal Distr	9 Sampling Distr	10 Conf Intervals	1st Sem Exam

Unit Plan Practice Test
Latin/Greek Root Words arch--------->ancient, example: archtype;         chrono------>time, example: chronology;             -dom----------->quantity/state, example: freedom               fer-------->carry, example: transfer;               gen--------->birth, example: generate;                 luc-------->light, example lucid;                 neo--------->new, example: neonatologist;                olig--------->few, example: oligarchy;              omni--------->all, omniscient;            sym--------->together, symbol; (Statistics connection)
AP Statistics Standards IV. Statistical Inference: Estimating population parameters and testing hypotheses (30% –40%) Statistical inference guides the selection of appropriate models. A. Estimation (point estimators and confidence intervals) Estimating population parameters and margins of error Properties of point estimators, including unbiasedness and variability Logic of confidence intervals, meaning of confidence level and confidence intervals, and properties of confidence intervals Large sample confidence interval for a proportion Large sample confidence interval for a difference between two proportions Confidence interval for a mean Confidence interval for a difference between two means (unpaired and paired)
Objectives Essential Question: Is there a way to get any researcher in the world to agree agree that your conclusions are reasonable even if they disagree with them? Ch 10.1 Statistical Inference Correctly use the term statistical inference. To draw a conclusion from data in a formal manner using well defined procedures Give the mathematical and a quick and dirty explanation of a confidence interval. Conf. Int. = estimate ± (margin of error) An estimate of a parameter based on a statistic accounting for uncertainty. Homefun:  -- Read section 10.1	Activities Lesson 1 Key Concept: Statistical inference Purpose: Gain an intuitive understanding of what statistical inference is. Stats Investigation (Teams of two):   Interactive Discussion: Objectives 1-2. What two things does a confidence interval give? Resources/Materials: two decks of cards
Stats Investigation 10.1: Estimating a Proportion Purpose: Determine a reasonable way to estimate a proportion for a population. Instructions: Write a rational hypothesis for what the proportion of red cards is in a deck of cards. Draw 10 samples with n=2 and 10 samples with n=20 from a deck of cards. Remove a card one at a time. Replace and shuffle the deck each time a card is drawn. Do this twice for each sample of two and twenty times for each sample of 20. Record the the proportion of red cards for each sample.  Create an interval around each sample which you feel has a high chance of containing the mean. Record your reasons for making the interval. Make two plots of all the intervals. One for n=2 and one for n=20. The plots should look like the one on page 511 minus the normal distribution picture.  Repeat the process for a second deck of cards. Questions /Conclusions: Which sample size tended to have the widest interval? Did every interval contain the true mean?
Essential Question: How can you express a measurement in an internationally accepted manner? Ch 10.1 Confidence Intervals State the type of distribution which confidence intervals are based on and sketch the appropriate picture of a confidence interval. (sampling distribution) State the 3 parts of a confidence interval and explain their meaning.  Confidence level probability a conf. int. will contain the parameter in numerous trials (p. 541) Estimate the parameter, generally a sample mean Margin of error 2*(ME) = (width of conf. int )   Calculate margin of error when standard deviation is known. ME = Z* [σp / (n)0.5] Describe what happens to the margin of error as confidence level (C) is increased. ME approaches infinity as C approaches 100% ME approaches zero as C approaches 0% Formally state the meaning of a level C confidence interval. (magic box p. 540) Tell why the margin of error is not a measure of accuracy in the data. The accuracy of a sample is typically unknown. (Remember, we would have to know the true mean to determine the accuracy of the sample.) ME depends on an arbitrarily determined value of C. (C usually = 95% but this is a convention not a mathematically derived principle.) State which form of error a margin of error represents. (Sampling Error) Be as one with the cautions listed on page 553. Homefun: 10.1, 10.3, 10.9, 10.11, --	Lesson 2 Key Concept: Confidence intervals   Purpose: Gain an intuitive understanding of what a confidence interval is and how it gives more information than just an estimate. Interactive Discussion: Objectives. for a large sample size with a known standard deviation: Conf Int = x-bar ± (z*) (sigma) / (squrt n)
Stats Investigation 10.2: Margin of Error Purpose: Determine the effects that  changes in confidence level, sample size, and standard deviation have on margin of error. Instructions: You will make three different plots as follows: Margin of error vs confidence level with sigma = 1 and n = 100. Vary confidence level from 60% to 99%.  Margin of error vs sigma with confidence level = 95%, and n = 100. Vary sigma from 1 to 5.  Margin of error vs sample size with confidence level = 95% and sigma = 1. Vary n from 100 to 500.  Questions /Conclusions: What is the effect of doubling the sigma and why? What is the effect of doubling the sample size and why? What is the effect of increasing the confidence level from 90% to 95%? Of the three items mentioned above, which one(s) are under the control of the experimenter? What type of error does the margin of error represent? Why is margin of error not a measure of accuracy? What sampling technique must be used if valid confidence intervals are calculated? Is a high confidence level necessarily more meaningful than a low confidence level?
AP Statistics Standards IV. Statistical Inference: Confirming models (continued) B. Tests of significance Logic of significance testing, null and alternative hypotheses; p-values; one- and two-sided tests; concepts of Type I and Type II errors; concept of power Large sample test for a proportion Large sample test for a mean
Essential Question: How does the US justice system compare to statistical analysis? Ch 10.2  Hypothesis or Significance Testing State the question asked by a significance test and the two possible answers. (Is there clear evidence of an effect?) State a generic null hypothesis. (There is no evidence of an effect.) State a generic alternative hypothesis. (There is clear evidence of an effect.) Give the null and alternative hypothesis for the American justice system. Define P-value. Assuming Ho is true, the probability of obtaining a test statistic as extreme or more extreme than the one obtained is ______. The smaller the p-value, the stronger the evidence is against Ho State the statistic used for indicating the level of significance. (Hint: it begins with a "p".) State the type of distribution used for tests of significance. The sampling distribution. Describe one tail and two tail tests from the standpoint of the null hypothesis and the p-values. Be as one with "z-test for a population mean" on page 572 Perform "z-test for a population mean" in the following ways: by hand (using the calculator only for basic mathematics) using z-tables. by hand, using the calculator only for basic mathematics and finding areas using the hypothesis testing features of the TI-83 using Minitab software Homefun: 10.29 - 10.32, 10.35, 10.37	Lesson 3 Key Concept: Significance Testing or Hypothesis Testing   Purpose: Learn the format for one of the key inference tools in statistics by comparing them to the U.S. justice system.   Interactive Discussion: Objectives. p-value definition: The probability of obtaining a test statistic as extreme or more extreme than the one obtained, assuming the null hypothesis is true.   Why is the null hypothesis rejected when the p-value is low?   How do the odds of correctly rejecting the null hypothesis compare to the odds of winning money in Las Vegas?   Can a good hypothesis test compensate for a faulty design of the system for collecting data?   What does a faulty design of a data collection system do to the probability of being right?   Web Page Resource: Type I and II Errors-Making Mistakes in the Justice System
Essential Question: Can a statistically significant hypothesis have no practical value? Ch 10.2 Alpha Levels Define the significance level, alpha--predetermined maximum acceptable p-value for rejecting the null hypothesis. Use one and two tailed tests of significance. one-tailed: area of tail = alpha two-tailed: area of each tail = (alpha) / 2     Use alpha to evaluate statistical significance.(p.577) Use a confidence interval (confidence level = C) as a significance or hypothesis test. (p.581) significance level = (1 - C) a confidence interval is essentially identical to a 2-tail hypothesis test. Describe the difference between statistical and practical significance. Even a tiny difference between x-bar of a sample and a population will be statistically significant if the sample size is large enough. Such a tiny difference may have no practical significance. State when statistical inference is not valid. (When based on data from a poorly designed study or experiment.)   Homefun: 10.45, 10.53, 10.55, 10.88	Lesson 4 Key Concept: Statistical standards of judgment   Purpose: learn how to use alpha levels in hypothesis tests.   Interactive Discussion: Objectives
Essential Question: How many ways can you make a an error of judgement? Ch 10.3 - 10.4 Types of Errors Pass the ultimate test of true statistics nerdhood: (Explain the difference between type 1 and type 2 errors.) Explain what a type 1 and type 2 error is for the American Justice System. Generate a truth table for a hypothesis test. State how alpha relates to the type 1 error. Name the hypothesis which is considered true when calculating alpha. Ho Name the hypothesis which is considered true when calculating beta. Ha Identify the areas representing the probabilities of type 2 and type 1 errors on a diagram of a hypothesis test showing a hypothetical sampling distribution. Determine alpha and beta. Power given: β = (1 - power) μHa = μHo: β  = (1 - α) μHa = (α boundary): β  = 50%   Determine the power of a hypothesis test. power = (1 - β) Beta given: power = (1 - β) μHa = μHo: power = α μHa = (α boundary): power = 50% Plot and interpret a power curve (power vs. separation between μHo and μHa) for a hypothesis test. sigmoidal shape at zero separation power =  alpha asymptote at 100% (as separation approaches infinity, power approaches 100%) State how power can be applied to quality testing in manufacturing.   Homefun: 10.67, 10.69, 10.71 Summative Assessment: Test Objectives 1-26	Lesson 5 Key Concept: Type I and type II errors, power of the test   Purpose: develop an intuition for the elements that affect the above. Interactive Discussion: Objectives. Web Page Resource: Type I and II Errors-Making Mistakes in the Justice System .Use the applet provided to simulate various types of errors