Math 250 Introduction to Probability and Statistics I

What is Statistics? Statistics as a subject provides a body of principles and methodology for designing the process of data collection summarizing and interpreting the data drawing conclusions and generalities.

Figure 1.1 (p. 2) Gallup Opinion Index

Statistics in our everyday life Employment data Consumer price index Gallup poll Quality and productivity improvement Testing medicines

Population and Sample A complete set of data is either physically impossible or from a practical standpoint not feasible (limitations of time, resources, facilities). A unit is a single entity, usually a person or an object, whose characteristics are of interest. The population of units is the complete collection of units about which information is sought. A statistical population is the set of measurements (or record of some qualitative trait) corresponding to the entire collection of units. A sample from a statistical population is the subset of measurements that are actually collected.

Table 1.1 (p. 9) Populations, Units, and Variables

How to select a sample? Must be impartial and objective Samples consisting of responses to call-in requests will, in general, not be representative of the population. The name of each unit written on a separate slip of paper and the slips placed in a box; slips can be drawn one at a time without replacement Using a random number table to select a sample

Table 1.2 (p. 12) Random Digits: A Portion of Table 1, Appendix B

Collection of Data Before collecting data Develop a statement of purpose that is both specific and unambiguous. (e.g., is the water safe for swimming) Translate the purpose into a measurement or a qualitative trait. (e.g., the amount of a radioactive material in water doesn’t exceed a certain safe limit)

Objectives of Statistics The major objectives of statistics are: 1.To make inferences about a population from an analysis of information contained in sample data. This includes assessments of the extent of uncertainty involved in these inferences. 2.To design the process and the extent of sampling so that the observations form a basis for drawing valid inferences.