1. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Section 8.1 Collecting Data

2. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Objectives o Distinguish between sampling techniques

3. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Collecting Data Most statistical studies are brought about by the desire to know the answer to a particular question. For instance, you might want to know which car gets the best gas mileage. The search for answers to many questions just like this is helped along by collecting data and then drawing conclusions.

4. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Population A population is the particular group of interest in a study.

5. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Data Data is information collected for a study.

6. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Census A census involves collecting data from every member of the population.

7. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Parameter A parameter is the numerical description of a particular population characteristic.

8. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Sample A sample is a subset of a population.

9. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Sample Statistic A sample statistic is the numerical description of a characteristic of a sample.

10. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Table 1: Population vs. Sample PopulationSample Whole groupPart of a group Group I want to know aboutGroup I do know about Numerical descriptions of characteristics are called parameters Numerical descriptions of characteristics are called statistics Parameters are generally unknown Statistics are always known Parameters are fixed Statistics vary with the sample chosen

11. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 1: Identifying Parts of a Survey Two shortened survey reports are given. In each report, identify the following: the population, the sample, the results, and whether the results represent a sample statistic or a population parameter. a.A headline about the rising obesity among young people led a school board to survey local high school students. Out of 231 students surveyed, 58% reported eating a “high fat” snack at least 4 times a week.

12. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 1: Identifying Parts of a Survey (cont.) b.A nonprofit organization interviewed 618 adult shoppers at malls across Louisiana about their views on obesity in youths. The resulting report stated that an estimated 48% of Louisiana adults are in favor of government regulation of “high fat” fast food options.

13. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 1: Identifying Parts of a Survey (cont.) Solution a.Population: local high school students Sample: the 231 students who were surveyed Results: 58% of students surveyed eat a “high fat” snack at least 4 times a week. The result refers to only those students who were surveyed, thus the result is a sample statistic.

14. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 1: Identifying Parts of a Survey (cont.) b.Population: Louisiana adults Sample: the 618 adult Louisiana mall shoppers who were surveyed Results: 48% of Louisiana adults are in favor of government regulation of “high fat” fast food options. The results refer to all Louisiana adults, thus this is a population parameter. This population parameter is an estimate based on the sample statistics, which were not reported.

15. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Representative Sample A representative sample is one that has the same relevant characteristics as the population and does not favor one group of the population over another.

16. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Random Sample A random sample is one in which every member of the population has an equal chance of being selected.

17. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Stratified Sample A stratified sample is one in which members of the population are divided into two or more subgroups, called strata, that share similar characteristics like age, gender, or ethnicity. A random sample from each stratum is then drawn.

18. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Skill Check #1 Can you think of some other ways to divide the cars into strata that might represent a broader scope of vehicles on the market? Answer: Answers will vary. For example: size of engine, manufacturer, make, safety rating, number of doors.

19. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Cluster Sample A cluster sample is one chosen by dividing the population into groups, called clusters, that are each similar to the entire population. The researcher then randomly selects some of the clusters. The sample consists of the data collected from every member of each cluster selected.

20. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Skill Check #2 For our mpg study, do you think this method would produce a good representative sample of vehicles if we allowed our clusters to be price ranges? Why or why not? Answer: Because cluster sampling is an “all from one group” method, comparing mpg’s from cars in only certain price ranges would not produce a representative sample.

21. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Systematic Sample A systematic sample is one chosen by selecting every n th member of the population.

22. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Skill Check #3 Identifying every 8 th car accessing the interstate on a particular entrance ramp during rush hour traffic is an example of systematic sampling for our fuel study. Can you identify any potential biases that we might need to be aware of when choosing the observation spot? Answer: The location of the entrance ramp might lend itself to having cars only on one end of the price scale depending on the businesses located in the area.

23. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Convenience Sample A convenience sample is one in which the sample is “convenient” to select. It is so named because it is convenient for the researcher.

24. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Skill Check #4 Earlier we mentioned gathering data from half the students in your class for our comparison of fuel- efficient cars. Do you think this example of convenience sampling would be an accurate picture of the population of cars driven in the United States? Answer: It is unlikely that students (or any age group for that matter) will drive a wide range of cars. Newer, more expensive cars are less likely to be driven by students and would not be well represented in the student sample.

25. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 2: Identifying Sampling Techniques Identify the sampling technique used to obtain a sample in each of the following situations. a.To conduct a survey on collegiate social life, you knock on every 5 th dorm room door on campus. b.Student ID numbers are randomly selected from a computer print out for free tickets to the championship game.

26. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 2: Identifying Sampling Techniques (cont.) c.Fourth grade reading levels across the county were analyzed by the school board by randomly selecting 25 fourth graders from each school in the county district. d.In order to determine what ice cream flavors would sell best, a grocery store polls shoppers that are in the frozen foods section. e.To determine the average number of cars per household, each household in 4 of the 20 local counties were sent a survey regarding car ownership.

27. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 2: Identifying Sampling Techniques (cont.) Solution a.Because the sample is obtained by choosing every n th dorm room, this is systematic sampling. This is a representative sample, as long as students were randomly assigned to dorm rooms and there are no hidden potential biases, like only males may live in every n th room. b.Since every member has an equal chance of being selected, this is random sampling.

28. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 2: Identifying Sampling Techniques (cont.) c.The students were divided into strata based on their schools and then a random sample from each school was chosen. This is stratified sampling. d.Because of the ease of choosing shoppers right in their own store, this is convenience sampling. In this case, convenience sampling is a viable method for gaining a representative sample since the store would be interested in knowing the thoughts of their customers.

29. HAWKES LEARNING Students Count. Success Matters. Copyright © 2015 by Hawkes Learning/Quant Systems, Inc. All rights reserved. Example 2: Identifying Sampling Techniques (cont.) e.Cluster sampling was used here because the counties are the natural clusters and all of the households in some of the counties received the surveys.