1. Lecture 1: Introduction
Statistics is concerned with
Collecting and presenting data to assist decision making
Obtaining reliable forecasts
Processing and analyzing data

2. Examples involving statistics
To predict the outcome of an election (Estimation and prediction)
To inspect the incoming goods from a supplier (One-sample hypothesis testing)
Developers of a new hypertension drug want to determine if the drug lowers blood pressure (Two-sample hypothesis testing)

3. Examples (cont’d)
In marketing, statistics is used to evaluate whether higher spending on advertising is justified (Simple linear regression)
To forecast economic indices, such as GNP, GDP, etc related to many factors (Multiple linear regression)

4. Key Definitions
A population (universe) is the collection of all members of a group
A sample is a portion of the population selected for analysis
A parameter is a numerical measure that describes a characteristic of a population
A statistic is a numerical measure that describes a characteristic of a sample

5. Population vs. Sample Population Sample a b c d b c ef gh i jk l m n
o p q rs t u v w
x y z
b c
g i n
o r u y
Measures used to describe a population are called parameters
Measures computed from sample data are called statistics

6. Examples Population All eligible voters
All light bulbs manufactured in a day
All patients with high blood pressure for a clinical study
Sample
1000 voters polled
100 light bulbs selected
200 hypertension patients enrolled for a clinical study

7. Two branches of statistics
Descriptive Statistics
Collecting, presenting, and characterizing data
Inferential Statistics
Drawing conclusions and/or making decisions concerning a population based only on sample data

8. Descriptive Statistics
Collect data
e.g., Survey
Present data
e.g., Tables and graphs
Characterize data
e.g., Sample mean =

9. Inferential statistics
Population
Sample
Use statistics to summarize features
Use parameters to summarize features
Drawing conclusions about a population based on sample results.

10. Two types of Inferential Statistics
Estimation
e.g., Estimate the population mean weight using the sample mean weight
Hypothesis testing
e.g., Test the claim that the population mean weight is 120 pounds

11. Reasons for Drawing a Sample
Less Time Consuming Than a Census
Less Costly to Administer Than a Census
Less Cumbersome and More Practical to Administer Than a Census of the Population

12. Types of Data Examples: Marital Status Political Party Eye Color
(Defined categories)
Examples:
Number of Children
Defects per hour
(Counted items)
Examples:
Weight
distance
(Measured characteristics)

13. Categorical random variables yield categorical responses
E.g. Are you married? Yes or No
Numerical random variables yield numerical responses
Discrete random variables yield numerical response that arise from a counting process
E.g. How many cars do you own? 3 cars
Continuous random variables yield numerical responses that arise from a measuring process
E.g. What is your weight? 130 pounds