§ 1.1

1. § 1.1 An Overview of Statistics

2. Data and Statistics Data consists of information coming from observations, counts, measurements, or responses. Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions. A population is the collection of all outcomes, responses, measurement, or counts that are of interest. A sample is a subset of a population.

3. Populations & Samples • Example: • In a recent survey, 250 college students at Union College were asked if they smoked cigarettes regularly. 35 of the students said yes. Identify the population and the sample. Responses of all students at Union College (population) Responses of students in survey (sample)

4. Parameters & Statistics A parameter is a numerical description of a population characteristic. A statistic is a numerical description of a sample characteristic. Parameter Population Statistic Sample

5. Parameters & Statistics • Example: • Decide whether the numerical value describes a population parameter or a sample statistic. a.) A recent survey of a sample of 450 college students reported that the average weekly income for students is $325. Because the average of $325 is based on a sample, this is a sample statistic. b.) The average weekly income for all students is $405. Because the average of $405 is based on a population, this is a population parameter.

6. Branches of Statistics The study of statistics has two major branches: descriptive statistics and inferential statistics. Statistics Inferentialstatistics Descriptivestatistics Involves the organization, summarization, and display of data. Involves using a sample to draw conclusions about a population.

7. Descriptive and Inferential Statistics • Example: • In a recent study, volunteers who had less than 6 hours of sleep were four times more likely to answer incorrectly on a science test than were participants who had at least 8 hours of sleep. Decide which part is the descriptive statistic and what conclusion might be drawn using inferential statistics. The statement “four times more likely to answer incorrectly” is a descriptive statistic. An inference drawn from the sample is that all individuals sleeping less than 6 hours are more likely to answer science question incorrectly than individuals who sleep at least 8 hours.

8. Note: The development of Inferential Statistics has occurred only since the early 1900’s. • Examples: • 1. The medical team that develops a new vaccine for a disease is interested in what would happen if the vaccine were administered to all people in the population. • 2. The marketing expert may test a product in a few “representative” areas, from the resulting information, he/she will draw conclusion about what would happen if the product were made available to all potential customers.

9. Population or Sample? • The age of each state governor A. Population B. Sample

10. Population or Sample? • The speed of every fifth car passing a police speed trap A. Population B. Sample

11. Population or Sample? • A survey of 500 students from a university with 10,000 students A. Population B. Sample

12. Population or Sample? • The annual salary for each employee at a company A. Population B. Sample

13. Population or Sample? • The cholesterol levels of 20 patients in a hospital with 100 patients A. Population B. Sample

14. Population or Sample? • The number of pets in each U.S. household A. Population B. Sample

15. Parameter or Statistic? • The average annual salary for 35 of a company’s 1200 accountants is $68,000. A. Parameter B. Statistic

16. Parameter or Statistic? • In a survey of a sample of high school students, 43% said that their mother has taught them the most about managing money. A. Parameter B. Statistic

17. Parameter or Statistic? • In 2007, the interest category for 12% of all new magazines was sports. A. Parameter B. Statistic

18. Inferential or Descriptive Statistics? • Fact: The following numbers of students passed this course in the past four years: 17, 19, 4, 20. • Is the following conclusion obtained from purely descriptive measures or by inferential methods? The last four semesters the instructor taught Probability & Statistics, an average of 15 people passed the class. A. Inferential B. Descriptive

19. Inferential or Descriptive Statistics? • Fact: The following numbers of students passed this course in the past four years: 17, 19, 4, 20. • Is the following conclusion obtained from purely descriptive measures or by inferential methods? The next time the instructor teaches Probability & Statistics, we can expect approximately 15 people to pass the class. A. Inferential B. Descriptive

20. Inferential or Descriptive Statistics? • Fact: The following numbers of students passed this course in the past four years: 17, 19, 4, 20. • Is the following conclusion obtained from purely descriptive measures or by inferential methods? This instructor will never pass more than 20 people in a Probability & Statistics class. A. Inferential B. Descriptive

21. Inferential or Descriptive Statistics? • Fact: The following numbers of students passed this course in the past four years: 17, 19, 4, 20. • Is the following conclusion obtained from purely descriptive measures or by inferential methods? The last four semesters the instructor taught Probability & Statistics, no more than 20 people passed the class. A. Inferential B. Descriptive

22. Inferential or Descriptive Statistics? • Fact: The following numbers of students passed this course in the past four years: 17, 19, 4, 20. • Is the following conclusion obtained from purely descriptive measures or by inferential methods? Only 4 people passed one semester because the instructor was in a bad mood the entire semester. A. Inferential B. Descriptive

23. Inferential or Descriptive Statistics? • Fact: The following numbers of students passed this course in the past four years: 17, 19, 4, 20. • Is the following conclusion obtained from purely descriptive measures or by inferential methods? The instructor passes so few people in his Probability & Statistics classes because he doesn't like teaching that class. A. Inferential B. Descriptive