1. § 1.1 An Overview of Statistics

3. 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.

4. 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)

5. 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

6. 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.

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

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

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

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

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

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

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

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

16.  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 Parameter or Statistic?

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

18.  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. InferentialB. Descriptive Inferential or Descriptive Statistics?

19.  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. InferentialB. Descriptive Inferential or Descriptive Statistics?

20.  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. InferentialB. Descriptive Inferential or Descriptive Statistics?

21.  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. InferentialB. Descriptive Inferential or Descriptive Statistics?

22.  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. InferentialB. Descriptive Inferential or Descriptive Statistics?

23.  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. InferentialB. Descriptive Inferential or Descriptive Statistics?