Mr. Rogers - AP Statistics Objectives

Syllabus	1st Quarter	2nd Quarter	3rd Quarter	4th Quarter
11 t-Test	12 Inf for Prop	13 Chi Test	14 Regession HT

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: Confirming models A. Confidence intervals IV. Statistical Inference: Confirming models (continued) B. Tests of significance C. Special case of normally distributed data  t-distribution Single sample t procedures Two sample (independent and matched pairs) t procedures
Objectives Essential Question: How can we account for the greater uncertainty of analyzing data when sample size is small and little is known about the population? Ch 11 State the 2 assumptions for drawing inferences about a population mean when sigma is not known. SRS Normal Distribution of the population (symmetrical with single peak) Calculate standard error of a statistic (std dev of sampling distr.) = s / ( n^.5 ) . Explain when a t statistic is used rather than a z score. Population Standard deviation not known Sample Size is Small Calculate t statistics. State the degrees of freedom for a t test. df = ( n-1 ) Construct confidence intervals using the t statistic. ME = t* s / ( n0.5 ) Perform one sample t-procedures: by hand (using the calculator only for basic mathematics) using t-tables. by hand, using the calculator only for basic mathematics and finding areas. tcdf (L,U,D) Lower t-value Upper t- value Degrees of Freedom   using the hypothesis testing features of the TI-83. Note that μ is the mean associated with Ha μo is the mean associated with Ho using Minitab software   Homefun (formative/summative assessment): 11.7, 11.9,  -- Read section	Activities Lesson 1 Key Concept:  How is t-Distribution used? Warm up: What conditions must be met to use a z-test? Interactive Discussion: Objectives. What conditions must be met to use a t-test and how does this differ from a z-test? Assuming a t-test is called for, what kinds of tests should be performed before using a t-test?
Essential Question: What is the single most powerful form of hypothesis testing and why? Matched Pairs Testing (Spanish Camp) Apply the t-test of significance to matched pairs (MP) situations. MP tests are 1 sample t-tests Ho: μ = 0 df = (number of pairs - 1) Be aware: you must establish that the population is approximately normally distributed. How to Establish That a Population is Normally Distributed Box Plot - symmetrical, box width smaller than a whisker's width Normal Quantile Plot - straight line Explain what is meant by a robust test or confidence interval. p-value  or confidence interval changes little if assumptions are violated. Be as one with the information in the "using t procedures" box on p.636. Be aware that outliers are very harmful to the t-test. Making a modified box plot of the data in order to look for outliers is a very good idea.     Homefun (formative/summative assessment):  11.13, 11.17, 11.21, 11.26	Lesson 2 Key Concept: How are Matched Pairs t-test used. Warm up questions (individuals): What two assumptions must be met to use a t-test? How do you know you have normally distributed data? What step must you take before using a t-test of any kind? Interactive Discussion: Set up confidence intervals and hypothesis tests for matched pairs. Problem Solving (Teams of two): Make a hypothesis test with matched pairs for a pre and post test situation--Spanish Camp
Essential Question: How can you determine if 2 populations differ if at the start you have no information? Ch 11 State the assumptions made for two-sample tests. (p. 650) SRS used for generating the sample independent - matched pairs violate independence normally distributed population Create confidence intervals and hypothesis test using two sample t procedures assuming that the sigmas of the two populations are unequal. This is the most conservative assumption. Ho: μ1 - μ2 = 0  but can also be written, Ho: μ1 = μ2   Test Statistic for  Hypothesis Testing Margin of Error for Confidence Interval t = (xbar1 - xbar2) - 0 (s12/n1 + s22/n2)0.5 ME = t* (s12/n1 + s22/n2) 0.5 Create confidence intervals and hypothesis test using two sample t procedures and the most conservative method of determining df. df = (the lower of n1 -1 or n2 - 1) Be aware of the more accurate way to calculate df as shown on page 659. This is the method used in the TI-83 calculator Perform two sample hypothesis t-procedures on the TI-83. State the key assumption required for using the pooled two-sample t-procedures. This is the method is an option in the TI-83 calculator. The sigmas of the two populations are the same   Homefun (formative/summative assessment): 11.33, 11.35, 11.37, 11.49:	Lesson 3 Essential Question:  How are two sample t-procedures -- no assumption made about the standard deviation being equal(p.624)--used?     Warm up questions (Individual): What two types of tools are used for inference? What type of distribution is used for making inferences? Interactive Discussion: Set up a hypothesis test for two samples and point out how it differs from Z-test   Problem Solving (Teams of two): Make a hypothesis test with 2 sample and matched pairs for a pre and post test situation--return to the Spanish Camp data.