Chapter 1:Statistics: The Art and Science of Learning from Data 1.1: How Can You Investigate Using Data? 1.2: We Learn about Populations Using Samples 1.3: What Role Do Computers Play in Statistics?

Section 1.1 Learning Objectives How Can You Investigate Using Data? 1. Data and examples of collecting data. 2. Define Statistics 3. Identify three aspects of a study

Learning Objective 1: Data Data is information we gather with experiments and with surveys. Example: Experiment on low carbohydrate diet Data could be measurements on subjects before and after the experiment Example: Survey on effectiveness of a TV ad Data could be percentage of people who went to Starbucks since the ad aired

Learning Objective 2: Define Statistics Statistics is the art and science of: Designing studies Analyzing resultant data Translating data into knowledge and understanding

Learning Objective 3: Statistical Methods Design: Planning how to obtain data Description: Summarizing the data Inference: Making decisions and predictions

Learning Objective 3: Descriptive Statistics Methods for summarizing data Summaries usually consist of graphs and numerical summaries of the data

Learning Objective 3: Examples of Design Statistics Design questions: How to conduct the experiment, or How to select people for the survey to insure trustworthy results Examples: Planning the methods for data collection to study the effects of Vitamin E on athletic strength For a marketing study, how do you select people for your survey to provide proper coverage

Learning Objective 3: Examples of Descriptive Statistics Description: Summarize the raw data and present it in a useful format (e.g., average, charts or graphs) Examples: A meteorologist constructs a graph showing the total precipitation in Bloomington, IL for each of the months of The average age of the students in a statistics class is 25 years.

Learning Objective 3: Inference Methods of making decisions or predictions about a populations based on information obtained from a sample.

Learning Objective 3: Examples of Inferential Statistics Inference: Make decisions or predictions based on the data Examples: There is a relationship between smoking cigarettes and getting emphysema. From past figures, it is predicted that 47% of the registered voters in Illinois will vote in the primary.

Section 1.2 Learning Objectives We Learn about Populations Using Samples 1. Subjects 2. Population and sample 3. Descriptive statistics and inferential statistics 4. Sample Statistics and Population Parameters 5. Randomness and Variability

Learning Objective 1: Subjects Subjects The entities that we measure in a study Subjects could be individuals, schools, rats, counties, widgets

Population Sample Learning Objective 2: Population and Samples Population: All subjects of interest Sample: Subset of the population for whom we have data

Learning Objective 2: Example: The Sample and the Population for an Exit Poll In California in 2003, a special election was held to consider whether Governor Gray Davis should be recalled from office. An exit poll sampled 3160 of the 8 million people who voted. Define the sample and the population for this exit poll. The population was the 8 million people who voted in the election. The sample was the 3160 voters who were interviewed in the exit poll.

Learning Objective 3 Descriptive vs. Inferential Statistics Descriptive Statistics refers to methods for summarizing the data. Summaries consist of graphs and numbers such as averages and percentages Inferential statistics refers to methods of making decisions or predictions about a population based on data obtained from a sample of that population.

Learning Objective 3: Descriptive Statistics Example Types of U.S. Households

Learning Objective 3: Inferential Statistics Example Calculating a confidence interval: By surveying 1000 likely voters, we find a sample proportion of 39% who approve of the job President Bush is doing. We are 95% confident that the population proportion of likely voters who approve of the job President Bush is doing is between 36% and 42%.

Learning Objective 4: Sample Statistics and Population Parameters A parameter is a numerical summary of the population Mean (µ) number of cigarettes smoked by all teenagers Proportion (p) of all teenagers who smoked in the last month

Learning Objective 4: Sample Statistics and Population Parameters A statistic is a numerical summary of a sample taken from the population Mean number of cigarettes smoked per day by a sample of teenagers Proportion of a sample of teenagers who smoked in the last month

Learning Objective 5: Randomness Simple Random Sampling: each subject in the population has the same chance of being included in the sample Randomness is crucial to insuring that the sample is representative of the population so that powerful inferences can be made

Learning Objective 5: Variability Measurements may vary from subject to subject, and Measurements may vary from sample to sample Predictions will therefore be more accurate for larger samples.

Section 1.3 What Role Do Computers Play in Statistics? Using Technology You, not technology, must select valid analyses Data files Large sets of data are typically organized in a spreadsheet format known as a data file Each row contains measurements for a particular subject Each column contains measurements for a particular characteristic Databases An existing archive collection of data files Sources should always be checked for reliability

Section 1.3 What Role Do Computers Play in Statistics? Applets A short application program for performing a specific task Useful for performing activities that illustrate the ideas of statistics