Lesson Objectives At the end of the lesson, students can: Recognize and define different sampling strategies Design sampling strategies Use the Random Digits Table and calculator to select random samples

How do we gather data? Surveys Opinion polls Interviews Studies ─ Observational ─ Retrospective (past) ─ Prospective (future) Experiments

How do we gather data? Observational study - observe outcomes without imposing any treatment Experiment - actively impose some treatment in order to observe the response

How do we gather data? Population: the entire group of individuals that we want information about

How do we gather data? Census: a complete count of the population

How do we gather data? Census: a complete count of the population  Why do we census?  How good is a census?

Activity Should We Census?

Why would we not census all the time? 1)Not accurate 2)Very expensive 3)Perhaps impossible 4)If using destructive sampling, you would destroy population Breaking strength of soda bottles Lifetime of flashlight batteries Safety ratings for cars

How do we gather data? Sample: A part of the population that we actually examine in order to gather information Use sample to generalize to population

How do we gather data? Sampling Design: refers to the method used to choose the sample from the population

How do we gather data? Sampling Frame: a list of every individual in the population

How do we gather data? Example: Mrs. Hood wants to find out what the Wake County high school students think about the effectiveness of their math teachers. a)Mrs. Hood sends out a survey to 1500 high school students randomly selected from the Wake County Public Schools records. 941 surveys are returned, indicating that 80% of the respondents believe their math teacher is effective. What is the population? What is the sampling frame?

Types of Sampling Design Simple Random Sample (SRS): consist of n individuals from the population chosen in such a way that every individual has an equal chance of being selected every set of n individuals has an equal chance of being selected

Types of Sampling Design Stratified Random Sample: population is divided into homogeneous groups called strata SRS’s are pulled from each strata

Types of Sampling Design Systematic Random Sample: select sample by following a systematic approach randomly select where to begin

Types of Sampling Design Cluster Sample: based upon location randomly pick a location & sample all there

Types of Sampling Design Multistage Sample: select successively smaller groups within the population in stages SRS used at each stage

The Pros and the Cons SRS Advantages – Unbiased – Easy Disadvantages – Large variance – May not be representative – Must have sampling frame (list of population)

The Pros and the Cons Stratified Random Sample Advantages – More precise unbiased estimator than SRS – Less variability – Cost reduced if strata already exists Disadvantages – Difficult to do if you must divide stratum – Formulas for SD & confidence intervals are more complicated – Need sampling frame

The Pros and the Cons Systematic Random Sample Advantages – Unbiased – Ensure that the sample is distributed across population – More efficient, cheaper, etc. Disadvantages – Large variance – Can be confounded by trend or cycle – Formulas are complicated

The Pros and the Cons Cluster Sample Advantages – Unbiased – Cost is reduced – Sampling frame may not be available (not needed) Disadvantages – Clusters may not be representative of population – Formulas are complicated

Identify the Sampling Design The Educational Testing Service (ETS) needed a sample of colleges. ETS first divided all colleges into groups of similar types (small public, small private, etc.) Then they randomly selected 3 colleges from each group.

Identify the Sampling Design A county commissioner wants to survey people in her district to determine their opinions on a particular law up for adoption. She decides to randomly select blocks in her district and then survey all who live on those blocks.

Identify the Sampling Design A local restaurant manager wants to survey customers about the service they receive. Each night the manager randomly chooses a number between 1 & 10. He then gives a survey to that customer, and to every 10 th customer after them, to fill it out before they leave.

Random Digits Table each entry is equally likely to be any of the 10 digits digits are independent of each other

Using the Random Digits Table Suppose your population consisted of these 20 people: 1) Aidan6) Fred 11) Kathy16) Paul 2) Bob7) Gloria 12) Lori 17) Shawnie 3) Chico8) Hannah 13) Matthew18) Tracy 4) Doug9) Israel14) Nan19) Uncle Sam 5) Edward10) Jung 15) Opus20) Vernon Use the Random Digits Table to select a sample of five from these people. Start at line

Using the Random Digits Table Suppose your population consisted of these 20 people: 1) Aidan6) Fred 11) Kathy16) Paul 2) Bob7) Gloria 12) Lori 17) Shawnie 3) Chico8) Hannah 13) Matthew18) Tracy 4) Doug9) Israel14) Nan19) Uncle Sam 5) Edward10) Jung 15) Opus20) Vernon Seed your calculator to Then select five from these people.

Homework Read Textbook pages Do exercises 4.1—pp /#1, 3, 5, 6, 8, 9, 11, 12, 15, 19, 21, Check answers to odd problems Be prepared for a HW quiz!

Lesson Objectives At the end of the lesson, students can: Recognize and define different sampling strategies Design sampling strategies Use the Random Digits Table and calculator to select random samples