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

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 III. Anticipating Patterns: (continued) D. Sampling distributions Sampling distribution of a sample proportion Sampling distribution of a sample mean Central Limit Theorem Sampling distribution of a difference between two independent sample proportions Sampling distribution of a difference between two independent sample means Simulation of sampling distributions
Objectives Essential Question: Can we describe the shape of a distribution of many samples of the same size even without knowing what the population's  distribution's shape is like? Ch 9 Describe the difference between a parameter and a statistic and give examples. Explain the use of p and p-hat. Given a sampling distribution, explain its meaning (p. 459). Determine if a statistic is unbiased (p. 468). Unbiased: sampling distr. mean = pop. mean (p.464) Compare variability to bias (targets p.465).   Which is worse, variability or bias? State how the variability of a statistic changes relative to population size. State which distribution has more variability, a sampling distribution or the population distribution it is based on? Calculate standard error (p. 587). (standard error) =  (s of sampling distr.)                               =  (s of population) / (n^.05) Homefun: 9.1 to 9.4  -- Read section 9.1 to 9.2	Activities Lesson 1 Key Concept: Characteristics of the sampling distribution Purpose: Form the foundation for tests of significance Interactive Discussion: Objectives .  Stats Investigation (Teams of two, see below):
Stats Investigation: Central Limit Theorem Purpose: Does the variability in the sampling distribution actually decrease as predicted by the central limit theorem?. Instructions: Go to http://intuitor.com/statistics/CentralLim.html and read the write up. Open the Central Limit Theorem Applet and set the number of samples slider to its maximum (max=2010). Run at least 10 simulations using a variety of sample sizes from 1 to 100. From the sampling distribution plot, record the sample size, standard deviation, and standard error. Analysis 1: Make a scatter plot of standard deviation vs. sample size. Perform linear regression and power regression on the data in the plot. Also make a residual plot for both forms of regression. Analysis 2: Make a second scatter plot of standard deviation vs. standard error. Perform linear regression, report the r-square value, and make a residual plot for this data. Questions /Conclusions: Which regression equation best fits the data in Analysis 1? Explain why? Explain the r-square value for the most appropriate equation in analysis 1. What is the predicted equation in analysis 2 and how does it compare to the regression equation. In analysis 2, what is the difference between the standard deviation of the sampling distribution and the standard error. Why do they have almost identical values? What is the difference between sample size and number of samples. Describe how increasing them influences the sampling distribution. What is the difference between the central limit theorem and the law of large numbers.
Ch 9 Calculate the mean and standard deviations of a binomial distribution for proportions. Compare the binomial distributions for proportions to the binomial distributions for counts. State why the binomial distribution is basically always a sampling distribution. State the two rules of thumb which must be met before using the normal approximation of the binomial distribution (pp. 473 & 475). Calculate the mean and standard deviation of a non-binomial sampling distribution (p. 483). State how the central limit theorem applies to sampling distributions. State how the law of large numbers applies to sampling distributions.   Homefun: 9.15, 9.17, 9.19, 9.25, 9.27, 9.31, 9.37 --  Read section 9.3	Lesson 2 Key Concept: The normal approximation of the binomial distribution Purpose: Apply the above Warm up (Teams of two):  Match sample size to the distribution Given sets of sample and population means for determine which ones are biased Interactive Discussion: Objectives. Note that with a large enough sample size the normal distribution of the sampling distribution starts looking spike-like. Problem Solving (Teams of two): Use the central limit theorem applet to understand the effects of sample size on normality.