Intro to Probability and Statistics UNIT 1 1

Intro to Probability and Statistics UNIT 1 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 is information we gather with experiments and with surveys. Example A: A researcher is doing an experiment on the effects a low carbohydrate diet. • What would the data be? Example B: Survey on effectiveness of a TV ad on Starbucks’ sales. • What would the data be?

Learning Objective 2: Define Statistics is the art and science of: • Designing studies / gathering data • Analyzing resultant data • Translating that data into knowledge and understanding What would the world look like without statistics?

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

Learning Objective 3: Design in Statistics DESIGN focuses on… • Methods for gathering data. • Designing surveys (observational) and experiments. • Writing survey questions • Determining how to best sample from a population

Learning Objective 3: Examples of Design Statistics Design questions: • • How to conduct the experiment? 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: Descriptive Statistics DESCRIPTIVE STATISTICS focuses on… • Methods for summarizing data • Summaries usually consist of graphs and numerical summaries of the data

Learning Objective 3: Examples of Descriptive Statistics Description questions: • What is the best way to summarize the results we obtained? (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 2005. • 40% of Seniors are enrolled to take prob/stats in the Spring 2015 semester.

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

Learning Objective 3: Examples of Inferential Statistics Inference questions: • What decisions or predictions can be made? 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 • Subjects • Population and sample • Descriptive statistics and inferential statistics • Sample Statistics and Population Parameters • Randomness and Variability

Learning Objective 1: Subjects • The entities that we measure in a study • Subjects are usually people and their responses, but could also be non-human such as schools, countries, or days. Anything that has measurable characteristics.

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

Learning Objective 2: Population and Samples Sample surveys such as the Gallup poll usually select about 1000 to 2500 Americans to represent the population. Rarely can data be taken for an entire population, as it is… • • • Physically impossible Time consuming Very expensive It is attempted by the US government in the form of a… CENSUS

Learning Objective 2: Example: The Sample and the Population for an Exit Poll In 2006 California gubernatorial election, ‘The Governator’, was running as the Republican candidate. An exit poll sampled 2705 voters and 56% said they voted for Arnold. There were nearly 7 million who cast their ballot in that election. 7 million who voted • The population was __________________. • The sample was ____________________. 2705 who were exit polled

Learning Objective 3 Descriptive vs. Inferential Statistics Descriptive Statistics refers to methods for summarizing the data. (Graphs, percentages, averages, etc. ) Inferential statistics refers to methods of making decisions or predictions with the data gathered.

Learning Objective 3: Descriptive Statistics Example Types of U. S. Households Descriptive Statistics “Here is a bar graph representing the percent of population diagnosed with diabetes based on income level. ” Inferential Statistics “Poorer people in America are more likely to have diabetes due to eating cheaper, unhealthy food. ”

Learning Objective 4: Confidence Intervals Margin of error tells us… The potential spread or range that a % may actually fall within. Inferential statistics says we can project a sample % as a representation of the entire population. The larger our sample the more confident we can be in the results.

Learning Objective 4: Example: Calculating a confidence interval: By surveying 980 likely voters, we find a sample proportion of 39% who approve of the job President Obama is doing. Inferential statistics says that we can project this % as a representation of the entire population of the U. S. We are able to be 95% confident that the population proportion of likely voters who approve of the job President Obama is doing has a 3% margin of error, so the actual approval rating ranges between _______% and _______%. 36 42

Learning Objective 4: Sample Statistics and Population Parameters A parameter is a numerical summary of the population (the entire population) • • Mean number of cigarettes smoked per day by all teenagers Proportion of all teenagers who smoked in the last month Parameter values are usually unknown and not able to be measured.

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 We take a sample for a sample statistic to represent the unknown parameters of the population.

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 describes the way measurements vary from… • subject to subject • sample to sample Predictions will therefore be more accurate when we take ______ LARGER samples.

Learning Objective 5: Variability Is there a problem? One study (A) surveys 1000 Arizona voters and finds that 48% are in favor a new bill to raise dog licensing fees. Another study (B) surveys a different 1000 Arizona voters and finds that only 44% are in favor of the new bill. Do the results conflict? Which is accurate?

Learning Objective 5: Variability Is there a problem? 1000 surveyed = 3% margin of error. So Study A at 48% = 45% 51% confidence interval And Study B at 44% = 41% 47% confidence interval 38 -39 -40 -41 -42 -43 -44 -45 -46 -47 -48 -49 -50 -51 -52 -53 -54 • • yes Were the populations the same? Were the samples the same? no, same amount but different people Is their overlap? Should bill lobbyists be discouraged? yes No, there is a chance it will still pass, since margin of error goes above 50%

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