SPA 3e_ Teachers Edition _ Ch 6

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PD LESSONS 6.1–6.3 Overview Watch the Lessons 6.1–6.3 overview video for guidance on teaching the content in these lessons. Find it in the Teacher’s Resource Materials by clicking on the link in the TE-book, logging into the Teacher’s Resource site, or accessing it on the TRFD. Lesson 6.1 What is a Sampling Distribution? L e A r n i n g T A r g e T S d Distinguish between a parameter and a statistic. d Create a sampling distribution using all possible samples from a small population. d Use the sampling distribution of a statistic to evaluate a claim about a parameter. Learning Target Key The problems in the test bank are keyed to the learning targets using these numbers: d 6.1.1 d 6.1.2 d 6.1.3 BELL RINGER What is the difference between random sampling and random assignment when collecting data? What inferences can be made in each case? Discuss your answers with a partner. AcT iviT y A penny for your thoughts? In this activity, your class will investigate how the mean year x and the proportion of pennies from the 2000s p^ vary from sample to sample, using a large population of pennies of various ages. 1 1. Have each member of the class randomly select 1 penny from the population and record the year of the penny with an “X” on the dotplot provided by your teacher. Return the penny to the population. Repeat this process until at least 100 pennies have been selected and recorded. This graph gives you an idea of what the population distribution of penny years looks like. 2. Have each member of the class take an SRS of 5 pennies from the population and note the year on each penny. • Record the average year of these 5 pennies with an “x” on a new class dotplot. Make sure this dotplot is on the same scale as the dotplot in Step 1 above. • Record the proportion of pennies from the 2000s with a “p^ ” on a different dotplot provided by your teacher. Return the pennies to the population. Repeat this process until there are at least 100 x's and 100 p^'s. 3. Repeat Step 2 with SRSs of size n 5 20. Make sure these dotplots are on the same scale as the corresponding dotplots from Step 2 above. 4. Compare the distribution of X (year of penny) with the two distributions of x (mean year). How are the distributions similar? How are they different? What effect does sample size seem to have on the shape, center, and variability of the distribution of x ? 5. Compare the two distributions of p^ . How are the distributions similar? How are they different? What effect does sample size seem to have on the shape, center, and variability of the distribution of p^ ? Teaching Tip This activity is the most important in the whole chapter and worth the time it takes because it introduces students to sampling distributions by simulating repeated sampling from a population. We recommend spending an entire class period on this activity as the introduction to this chapter. As an alternative, consider starting it in Chapter 4 or Chapter 5 and do a little each day, as explained in the Activity Overview document. 400 Starnes_3e_CH06_398-449_Final.indd 400 Activity Overview Time: 40–50 minutes Materials: Large chart paper and markers, dot stickers, or bingo daubers to make a dotplot. Alternatively, you can make a class dotplot on the whiteboard. You will also need a population of pennies. You need a minimum of 600 pennies, but 1000 or more is ideal. Teaching Advice: See the Lesson 6.1 Activity overview and activity handout. To estimate the mean income of U.S. residents with a college degree, the Current Population Survey (CPS) selected a random sample of more than 60,000 people with at least a bachelor’s degree. The mean income in the sample was $69,609. 2 How close is this estimate to the mean income for all members of the population? To find out how an estimate varies from sample to sample, we want to gain some understanding of sampling distributions. TRM Lesson 6.1 Activity Overview for Teachers TRM Lesson 6.1 Activity Handout A detailed Activity Overview document with sample graphs for teachers, as well as an Activity Handout for students, is available for this important activity. Consider giving the handout to your students so they don’t look ahead in their books for ideas and hints. You can find these resources by clicking on the link in the TE-book, logging into the Teacher’s Resource site, or accessing them on the TRFD. 18/08/16 4:57 PMStarnes_3e_CH0 400 C H A P T E R 6 • Sampling Distributions Starnes_3e_ATE_CH06_398-449_v3.indd 400 11/01/17 3:53 PM
L E S S O N 6.1 • What Is a Sampling Distribution? 401 Parameters and Statistics For the sample of college graduates contacted by the CPS, the mean income was x 5 $69,609. The number $69,609 is a statistic because it describes this one sample. The population that the researchers want to draw conclusions about is all U.S. college graduates. In this case, the parameter of interest is the mean income m of the population of all college graduates. DEFINITION Statistic, Parameter A statistic is a number that describes some characteristic of a sample. A parameter is a number that describes some characteristic of the population. Because we can’t examine the entire population, the value of a parameter is usually unknown. To estimate the value of the parameter, we use a statistic calculated using data from a random sample of the population. Remember s and p: statistics come from samples, and parameters come from populations. The notation we use should reflect this distinction. For example, we write m (the Greek letter mu) for the population mean and x for the sample mean. The table lists some additional examples of statistics and their corresponding parameters. Teaching Tip Remind students that we have seen a “hat” before in this course. The estimated value of y is denoted y^ . Likewise, the estimated value of p is denoted p^ . TRM chapter 6 Alternate Examples You can find the Alternate Examples for this chapter in Microsoft Word format by clicking the link in the TE-book, logging into the Teacher’s Resource site, or accessing it on the TRFD. Alternate Example Lesson 6.1 Sample statistic Population parameter x (the sample mean) estimates m (the population mean) p^ (the sample proportion) estimates p (the population proportion) s (the sample SD) estimates s (the population SD) How are teens different from turkeys? Parameters and statistics PROBLEM: Identify the population, the parameter, the sample, and the statistic in each of the following settings: (a) A Pew Research Center poll asked 1102 12- to 17-year-olds in the United States if they have a cell phone. Of the respondents, 71% said “Yes.” 3 (b) Tom is roasting a large turkey breast for a holiday meal. He wants to be sure that the turkey is safe to eat, which requires a minimum internal temperature of 165°F. Tom uses a thermometer to measure the temperature of the turkey breast at four randomly chosen points. The minimum reading he gets is 170°F. e XAMPLe SOLUTION: (a) Population: all 12- to 17-year-olds in the United States. Parameter: p 5 the proportion of all 12- to 17-year-olds with cell phones. Sample: the 1102 12- to 17-year-olds contacted. Statistic: the sample proportion with a cell phone, p^ 5 0.71. (b) Population: all possible locations in the turkey breast. Parameter: the true minimum temperature in all possible locations. Sample: the four randomly chosen locations. Statistic: the sample minimum, 170°F. FOR PRACTICE TRY EXERCISE 1. Pictures of coworkers? Parameters and statistics PROBLEM: Identify the population, parameter, sample, and statistic in each of the following settings: (a) A professional photographer is interested in the average number of photographs she took per day last year. She randomly selected 10 days from the year and recorded the number of photographs she took on each of the 10 days. The average number of photographs she took on those 10 days is 831.2 photos. (b) A Pew Research Center Poll asked a random sample of U.S. adults 18 or older whether they prefer to have a male coworker, a female coworker, or whether it doesn’t matter. Of the 2002 respondents, 77% said it “doesn’t matter.” SOLUTION: 18/08/16 4:57 PMStarnes_3e_CH06_398-449_Final.indd 401 Teaching Tip 18/08/16 4:58 PM Point out the phrase “who would say” in the solution to part (b) of the alternate example. It is not correct to say that the parameter is “the true proportion of all U.S. adults 18 or older who said it ‘doesn’t matter.’” The true proportion who said it doesn’t matter is 77%, which is the statistic (the sample proportion). Tell students to be careful about using the past tense to describe parameters! (a) Population: all days last year. Parameter: m, the true average number of photographs per day the photographer took over all days last year. Sample: the 10 randomly chosen days. Statistic: the sample mean number of photographs per day, x 5 831.2 photos. (b) Population: all U.S. adults 18 or older. Parameter: p 5 the true proportion of all U.S. adults 18 or older who would say it “doesn’t matter.” Sample: the 2002 U.S. adults 18 or older who participated in the survey. Statistic: the sample proportion who said it “doesn’t matter,” p^ 5 0.77. L E S S O N 6.1 • What Is a Sampling Distribution? 401 Starnes_3e_ATE_CH06_398-449_v3.indd 401 11/01/17 3:53 PM
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SPA 3e_ Teachers Edition _ Ch 6

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