SP 2015

Journal Prompt: Describe 5 things that might be wrong with Catbert’s claims

When the next slide is shown Pick a number from those displayed Write it down on your journal page

How many students in this class selected each number? What percentage selected each number?

How did your class compare? Typically about: 75% will choose 3 20% will choose 2 or 4 5% will choose 1

The study of numerical data (information)

 A sample is a collection of data from some fraction of a population.  It allows us to learn about the entire population by studying a relatively small portion of the population.

 A census is when every individual in the population is measured.  Not difficult if your population is Mrs. Otap’s 4 th Block.  Imagine your population is all household in South Carolina.  What would happen by the them you collected data from the entire population? (does the wording matter or did that last one make sense?)  Would there be some households that could be easily missed?

 Suppose you are interested in knowing the mean height for everyone in your school. ◦ What would a census tell you? ◦ How close would a sample size of one less student that the population be to the mean of the population? ◦ What about ten less students? ◦ If you took a sample of 100 and another sample of 10, which mean would be closer to the population?

 In general, a larger sample size will result in a more accurate estimate of the population.  When the population is very large, larger samples will not produce significantly better results and are usually more expensive or difficult to obtain.  A balance is usually made, not too small to sacrifice accuracy, and not too large to sacrifice cost.  For very large populations a sample size in the hundreds is normally sufficient.

 Making sure that a sample is truly random means that the person taking the sample has no control over who is selected.  When a sample is not random a bias could appear. This means that some individuals are somehow favored over others in the population.

Each individual has an equal chance of being selected Example: High School Students  Step 1: Write each student’s name on a slip of paper  Step 2: Mix the papers up in a box  Step 3: Draw names/slips from the box (Is this feasible for Wando? Other ideas?)

 Describe a method that would ensure your sample of 5 students from this class will be a simple random sample. Compare and discuss your method with others in the class.

 Random Numbers are a primary tool in selecting SRS.  You can get random numbers from your TI- 84 calculator.  Books of random numbers have been published. Page 834  Websites exist which provide truly random numbers.

Select random groups and interview every member of the selected groups Example: High School Students  Step 1: Randomly select classes  Step 2: Interview every student in the selected classes

An appropriate rule or pattern is used to make selections Example:  Step 1: Sort students alphabetically by last name, first name.  Step 2: Select every 8 th name on the list

Population is divided into subpopulations or strata and a random sample taken from each subgroup Example: High School Students  Step 1: divide students by grade level  Step 2: use an appropriate method to take a random sample from each subgroup

 Easy  Example: Survey your friends

 Def: Bias from people choosing if they participate  Example: Lunch Room ask each person if they want to take a quick survey

 Def: Bias resulting from a large number not responding  Ex: Chose 1234, only half the students gave answer

 Def: Anything in a survey design that influences responses  Example: Raise your hand if you are failing this class  Do you want this ugly yellow or this pretty blue for our shirts?

 Some part of population is under represented  Example: Lack of lower income individuals vote in presidential election

1. Determine a)What information you need to gather b)What size sample you want to use c)How you will collect the information 2. Create the Survey a)Brainstorm questions b)Read through proposed questions and fine tune the wording c)Put the questions in the order you want them to be on the survey d)Review the survey and determine if questions should be removed or added e)Construct your final list of survey questions 3. Identify the Sample to be Used 4. Collect the data 5. Organize data (table/chart) 6. Analyze data & draw conclusions

1) As LARGE as possible, A study with 100 people is going to be a more authentic study than a study with 10 people. 2) REPRESENTATIVE of the larger population you are studying If your study is favorite singer among 7th graders, only survey 7th graders! Don't ask 8th graders, your parents, baby cousins, etc. 3) RANDOMLY selected If your study is favorite sports team, don't ask only Yankees fans. 4) UNBIASED (fair)

 Question 1 – Do you like this ugly yellow shirt, or is blue a color for our T-shirt?  Question 2 – Which color do you prefer for our t-shirt? Yellow or blue?

 Plan 1 – Go to the supermarket and ask 50 people.  Plan 2 – Go to Hunter Mountain Ski Resort and ask 50 people.

CW 6) You want to conduct a study to determine the average student height at OMS. Determine if the potential sample is unbiased/fair or biased/unfair, explain your reasoning. Sample UnbiasedBiased FairUnfair a)Every 3rd student entering school on Monday. b)The basketball team c)The entire 8th grade class d) Every 10 th person selected from an alphabetical list of all students e)All girls at OMS f) The 1 st three students who report to the nurse on Monday

Sample Un- biased Biased FairUnfair a) The gym, after a game b)The library c)The lunchroom d) The cheerleaders’ meeting e) The next meeting of the prom committee f) An advisory class chosen at random