Population: the entire group of individuals that we want information about   Census: a complete count of the population Sample: A part of the population that we actually examine in order to gather information (Use sample to generalize to population) Sampling Design: refers to the method used to choose the sample from the population Sampling Frame: a list of every individual in the population

Judgmental Sample Selecting a sample based on who you think should be included. (Not a good sampling design) Convenience Sample Selecting a sample that is easy to get. (Not a good sampling design) Simple Random Sample- every possible sample of size n has an equal chance of being selected

Simple Random Sample (SRS) Suppose we were to take an SRS of 100 CHS students – put each students’ name in a hat. Then randomly select 100 names from the hat. Each student has the same chance to be selected! every possible sample of size n has an equal chance of being selected Randomly select subjects Not only does each student has the same chance to be selected – but every possible group of 100 students has the same chance to be selected! Therefore, it has to be possible for all 100 students to be juniors in order for it to be an SRS!

Is the following a SRS?? There are 15 classrooms in the math wing to sample from during 4th period. Each class has exactly 25 students. A sample of 30 students is chosen by the following procedure: Each of the 15 teachers selects 2 students from his/her classroom to be in the sample by numbering all the students from 1 to 25, then using the TI-nspire calculator to randomly select two different numbers between 1 and 25. The 2 students with those numbers are in the sample. Did this procedure give a simple random sample of 30 students from the math wing 4th period? NO!

Systematic Random Sample- Selects every ith item of the population (randomly select where to begin) Cluster Random Sample- Usually based upon location, randomly pick a location & sample all there Population is broken into subgroups that are small images of the target population and everyone in the selected subgroups is sampled. Stratified Random Sample- population is divided into homogeneous groups called strata, SRS’s are pulled from each strata

Cluster vs. Stratified In a cluster sample you randomly select a cluster (usually heterogeneous groups) and sample everyone in that cluster In a stratified sample you divide the population into stratas (usually homogeneous groups) and then randomly select a few from each strata.

Multi-Stage Random Sample- select successively smaller groups within the population in stages, SRS used at each stage

Review) Ten percent of U. S. households contain 5 or more people Review) Ten percent of U.S. households contain 5 or more people. You want to simulate choosing a household at random and recording whether or not it contains 5 or more people. Circle all correct assignments of digits for this simulation. A) Odd = Yes (5 or more people); Even = No (not 5 or more people) B) 0 = Yes; 1,2,3,4,5,6,7,8,9 = No C) 00 – 09 = Yes; 10 – 99 = No D) 5,6,7,8,9 = Yes; 0,1,2,3,4 = No E) 01 – 10 = Yes; 11 – 99 = No

Review) To simulate a toss of a coin we let the digits 0, 1, 2, 3, and 4 correspond to a head and the digits 5, 6, 7, 8, and 9 correspond to a tail. Consider the following game: We are going to toss the coin until we either get a head or we get two tails in a row, whichever comes first. If it takes us one toss to get the head we win $2, if it takes us two tosses we win $1, and if we get two tails in a row we win nothing. Use the entire following sequence of random digits: 1 2 9 7 5 1 3 2 5 8 4 5 1 4 4 Based on this simulation what is the expected number of tosses for the game? a. 1.364 b. 1.273 c. 1 d. 0.636 e. 0.818 A

Identify the sampling design 1) 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. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample C

Identify the sampling design 2) A statistics teacher wants to know how her students feel about an introductory Stat course. She has 200 students total but doesn’t want to ask them all. She decides to administer a survey to a random sample of students taking the course using the following procedure: Each student is given a number from 1-200. She then randomly selects 50 numbers using the TI-nspire calculator. The students selected get to be in the sample. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample A

Identify the sampling design 3) 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 10th customer after them, to fill it out before they leave. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample B

Identify the sampling design 4)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. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample D

Identify the sampling design 5) Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are three high schools in the district, each with grades 9 – 12. The school board pools all of the students together and randomly samples 250 students. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample A

Identify the sampling design 6) A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production. Then they randomly select 5 bags from each case and inspect then contents. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample E

Identify the sampling design 7) There are 10 classrooms in the math wing to sample from during 4th period. Each class has exactly 20 students. A sample of 30 students is chosen by the following procedure: Each student is given a number 1-200 and the using a TI-nspire calculator 30 numbers are randomly generated. The 30 students with those numbers are in the sample. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample A

Identify the sampling design 8) In doing an investigation of health care coverage in a metropolitan area, a researcher surveys every resident in a randomly selected three-block area. SRS Systematic random sample Cluster random sample Stratified random sample Multi-Stage random sample C