SPA 3e_ Teachers Edition _ Ch 6

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6 Sampling Distributions Please read the Introduction to the Teacher’s Edition. It will help prepare you for teaching this course, as it includes a lot of helpful information and advice. The Big Picture This chapter focuses on sampling distributions. A sampling distribution describes the possible values of a statistic such as the sample mean x or the sample proportion p^ and how often they occur. Three characteristics of sampling distributions will be examined in detail: center, variability, and shape. These are the same three characteristics used in Chapter 1 to describe distributions of quantitative data. The mean and standard deviation measure the center and variability of sampling distributions. The shapes of sampling distributions will be described with the same terms in use since Chapter 1: skewed left, skewed right, symmetric, mound-shaped, and a new term from Chapter 5: approximately normal. The variables examined in this chapter are examples of random variables, which were introduced in Chapter 5. The sample count X is a binomial random variable and is therefore discrete. The sample proportion p^ is closely related to the sample count X. Finally, the sample mean x is a continuous random variable. The process of making a conclusion about a population based on the data in a sample is called statistical inference. Chapter 6 lays the foundation for the statistical inference techniques learned in Chapters 7–10. Chapter 6 describes the sampling distribution of a sample statistic when certain characteristics are known about a population. In future chapters, we will test claims and estimate population parameters using what we have learned about these sampling distributions, even when population characteristics are unknown. The sampling distribution of p^ , the sample proportion, and x, the sample mean, are of particular importance for Chapters 7–9. In those chapters, the values of unknown population proportions and population means will be estimated, and claims about them will be tested. Furthermore, estimates will be made and claims will be tested about the difference in two proportions and the difference in two means. Pacing and Assignment Guide Day Lesson Learning Targets/Classroom Activities Suggested Assignment 1 Ch. 6 Introduction Lesson 6.1 Activity: A penny for your thoughts? None 2 6.1 What Is a Sampling Distribution? • Distinguish between a parameter and a statistic. • Create a sampling distribution using all possible samples from a small population. • Use the sampling distribution of a statistic to evaluate a claim about a parameter. 1–15 odd, 19 3 6.2 Introduction Lesson 6.2 Activity: How many craft sticks are in the bag? None 4 6.2 Sampling Distributions: Center and Variability 5 6.3 Sampling Distribution of a Sample Count (The Normal Approximation to the Binomial Distribution) • Determine if a statistic is an unbiased estimator of a population parameter. • Describe the relationship between sample size and the variability of a statistic. • Calculate the mean and the standard deviation of the sampling distribution of a sample count and interpret the standard deviation. • Determine if the sampling distribution of a sample count is approximately normal. • If appropriate, use the normal approximation to the binomial distribution to calculate probabilities involving a sample count. 1–15 odd, 19 1–15 odd, 19 6-2 C H A P T E R 6 • Sampling Distributions Starnes_3e_ATE_CH06_398-449_v3.indd 2 11/01/17 3:51 PM
6 Flex Day Consider giving Quiz 6A: Lessons 6.1–6.3, showing one or more of the online videos listed in the Additional Chapter 6 Resources, or re-teaching (if needed). Optional assignment: 6.1 Ex12, 6.2 Ex10, 6.2 Ex14, 6.3 Ex14 7 6.4 The Sampling Distribution of the Sample Proportion • Calculate the mean and standard deviation of the sampling distribution of a sample proportion p^ and interpret the standard deviation. • Determine if the sampling distribution of p^ is approximately normal. • If appropriate, use a normal distribution to calculate probabilities involving p^ . 1–15 odd, 19 8 6.5 The Sampling Distribution of the Sample Mean • Find the mean and standard deviation of the sampling distribution of a sample mean x and interpret the standard deviation. • Use a normal distribution to calculate probabilities involving x when sampling from a normal population. 1–15 odd, 19 9 6.6 The Central Limit Theorem • Determine if the sampling distribution of x is approximately normal when sampling from a non-normal population. • If appropriate, use a normal distribution to calculate probabilities involving x. 1–15 odd, 19 10 Flex Day This is a great day to have students work in groups on the STATS applied! at the end of Lesson 6.6. Also consider showing one or more of the online videos listed in the Additional Chapter 6 Resources, giving Quiz 6B: Lessons 6.4–6.6, or re-teaching (if needed). Optional assignment: 6.4 Ex14, 6.5 Ex10, 6.5 Ex12, 6.6 Ex10, 6.6 Ex12 11 Ch. 6 Review Ch. 6 Practice Test Ch. 6 Review Exercises 1–6 12 Ch. 6 Test Ch. 6 Test To save time, it is possible to skip Lessons 6.2 and 6.3 without losing much continuity with future chapters. However, the other lessons in this chapter are crucial to understanding much of the remainder of the course. Four kinds of exercises end each lesson: Mastering Concepts and Skills, Applying the Concepts, Extending the Concepts, and Recycle and Review. They have been written so that assigning the odd-numbered exercises provides appropriate practice. Mastering Concepts and Skills exercises address a single learning target, while Applying the Concepts exercises address two or more learning targets. Recycle and Review exercises reinforce concepts learned earlier. For exceptional or motivated students, Extending the Concepts exercises are a good way to differentiate instruction. The even-numbered exercises form a pair with the preceding odd exercise in the Mastering Concepts and Skills and Applying the Concepts sections so that another full assignment can be created from the even-numbered exercises of these types. Consider using the even-numbered exercises to spiral into future lessons, for re-teaching, or as additional practice for students. The answers to the odd-numbered exercises appear in the back of the student textbook, while the answers to the even-numbered exercises do not. The answers to all of the Chapter Review Exercises and the Chapter Test are in the back of the student textbook so that students can check their own progress. C H A P T E R 6 • Sampling Distributions 6-3 Starnes_3e_ATE_CH06_398-449_v3.indd 3 11/01/17 3:51 PM
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