Information from Samples

1. Math Alliance Project Information from Samples Alliance ClassJanuary 17, 2012

2. Math Alliance Project AgendaLessons for Student PostersCCSS Grade 7 StatisticsTypes of SamplingSampling Activities

3. Math Alliance Project Lesson Plans for Student Posters Day 1: Brainstorming 2/17 Day 2: Sort and Classify Questions 2/17 Day 3: Planning 2/17 Day 4: Data Collecting 3/17 Day 5: Graphs 3/17 Day 6: Poster 4/1 or spring break

4. Math Alliance Project WALT • Develop an understanding of 7.SP.1 and 2. • Understand the different methods of collecting a sample from a population. • Understand the need for random selection of a sample.

5. Math Alliance Project Success Criteria • When I am able to clearly explain and provide an example for CCSS standard 7.SP. 1and 2. • When I am able to identify the different methods of sampling and explain why random sampling is important.

6. Math Alliance Project CCSS 7th Grade Statistics Domain  Use random sampling to draw inferences about a population. • Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7. Math Alliance Project CCSS Grade 7 Statistics Domain 2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

8. Math Alliance Project Standard 7.SP.1 • Read Standard 7.SP.1 • Divide your paper in half. On one side, rephrase this standard and on the other side, provide an example. • Share with your partner.

9. Math Alliance Project Standard 7.SP.2 • Read standard 7.SP.2 • Divide your paper in half. On one side, rephrase this standard and on the other side, provide an example. • Share with your partner.

10. Math Alliance Project Types of Sampling • Simple Random Sample • Stratified Random Sample • Cluster sampling • Systematic • Convenience

11. Math Alliance Project Simple Random Sample • Every subset of a specified size n from the population has an equal chance of being selected

12. Math Alliance Project Stratified Random Sample • The population is divided into two or more groups called strata, according to some criterion, such as geographic location, grade level, age, or income, and subsamples are randomly selected from each strata.

13. Math Alliance Project Cluster Sample • The population is divided into subgroups (clusters) like families. A simple random sample is taken of the subgroups and then all members of the cluster selected are surveyed.

14. Math Alliance Project Systematic Sample • Every kth member ( for example: every 10th person) is selected from a list of all population members.

15. Math Alliance Project Convenience Sample • Selection of whichever individuals are easiest to reach • It is done at the “convenience” of the researcher

16. Math Alliance Project Errors in Sampling • Non-Observation Errors • Sampling error: naturally occurs • Coverage error: people sampled do not match the population of interest • Underrepresentation • Non-response: won’t or can’t participate

17. Math Alliance Project Errors of Observation • Interview error- interaction between interviewer and person being surveyed • Respondent error: respondents have difficult time answering the question • Measurement error: inaccurate responses when person doesn’t understand question or poorly worded question • Errors in data collection

18. Math Alliance Project Random Rectangles • When given the cue turn the paper over. Within 5 seconds make a guess for the average area of the rectangles. • When given the cue turn the paper over. Select 5 rectangles you think are representative of the rectangles on the page. Write the rectangle numbers and their areas. Compute the average of the 5 rectangles.

19. Math Alliance Project Random Rectangles • Use the random-number generator on the graphing calculator to select five different numbers from 1 to 100. Write down the five numbers and the area of each of the five rectangles. Find the area of the five rectangles.

20. Math Alliance Project Random Rectangles Report the three answers that you found for the average of the rectangles. • Guess • Representative sample • Random sample At your table construct 3 box plots

21. Math Alliance Project Random Rectangles Compare the three box plots. Describe any similarities and differences. Compare the medians of the three box plots to the actual area of all 100 rectangles.

22. Math Alliance Project Practice At your table explain how you would conduct: • A simple random sample of teachers in our class • A stratified random sample of teachers in our class • A systematic sample of teachers in our class

23. Math Alliance Project Practice To conduct a survey of long-distance calling patterns, a researcher opens a telephone book to a random page, closes his eyes, puts his finger down on the page, and then reads off the next 50 names. Which of the following are true statements? I. The survey design incorporates chance II. The procedure results in a simple random sample III. The procedure could easily result in selection bias a) I and II b) I and III c) II and III d) I, II and III e) None of the above gives the complete set of true responses

24. Math Alliance Project Practice A large elementary school has 15 classrooms, with 24 children in each classroom. A sample of 30 children is chosen by the following procedure: Each of the 15 teachers selects 2 children from his or her classroom to be in the sample by numbering the children from 1 to 24, using a random digit table to select two different random numbers between 01 and 24. The 2 children with those numbers are in the sample. Did this procedure give a simple random sample of 30 children from the elementary school? a) No, because the teachers were not selected randomly b) No, because not all possible groups of 30 children had the same chance of being chosen c) No, because not all children had the same chance of being chosen d) Yes, because each child had the same chance of being chosen e) Yes, because the numbers were assigned randomly to the children

25. Math Alliance Project Visual Bias • Pull the slide until the line on the slide looks as if it is the same length as the line on the face of the card. • Turn the card over and read the length • Record this length and report it when asked.

26. Math Alliance Project Bias Experiment • Report your length. • Construct a box plot of the class data. • Compare the box plot to the actual length. • Do the reported lengths tend to be the same? Do they appear to be systematically too long or too short?

27. Math Alliance Project Homework • CMP Samples and Population (Handout) • Read pp. 26 to 32. • Do Problem 2.3 page 32 • Use the spinners on page 31 and a paper clip as the spinner to generate the random numbers that are needed for A1 and 2.