Choosing the Correct Inference Procedure: Flow Chart Activity
Overview
This leads students through a G_S_C_E activity to create an Inference Procedure Flow chart for AP Statistics. great for summarizing inference procedures and helping students prepare for the AP exam. This activity is best done face to face but can be done online as well using flip grid, post-it notes and flow chart sties and weel as good docs or one note.
Task 1: How to Choose an Appropriate Inference Procedure: Make a Flow Chart
You can do this activity face to face in small groups or online individually or thorugh a collaborative document. If doing face to face, provide paper and markers, crayons, scissors, glue so students can create. If doing online provide links to Flipgrid and create a place for them to share a photo or document of their work and make a video. They can also use a post-it note app or google document to create a flow chart online alone or coolaboratively.
This lesson should be completed in one class meeting with time outside of class to finaize the product and create the Flipgrid video.
Learning Targets:
I can organize the learning I have gained with regard to Inference Procedures (make the flow chart) in a way will help me decide which inference procedure to use in any inference procedure problem.
I can use the Flow chart to help me decide which inference procedure to use and then to complete the problem.
We have spent a few weeks learning about Inference. We have spent time on hypothesis testing and confidence intervals. Your job today, is to create a flow chart to help you decide which Inference procedure to use in solving problems. Your should also include HOW to use each inference procedure in you flow chart. The following pages will walk you thorugh this process. Please keep a written record of each step. I have provided optional links to ONLINE options for keeping track of your work and notes.
First, lets look at some problems we may have to solve.....
DO not try to solve these, just read for now.
- A teacher wants to know if the method of instruction affects how well students learn. Using two classes of the same level of statistics, she teaches one class using lecture only and the other class using lecture and group work. She measures the level of learning by giving both classes the same test.
- A student of political science wished to determine whether there is a relationship between the gender of a student and their political affiliation.
- A student wishes to test if SUV drivers in his state are more likely to be male than female. He randomly selects 50 students from a list of registered SUV drivers and records their gender.
- Your friend in Portland claims that many drivers who pass her while she awaits the school bus are talking on a cell phone. You think it is a worse problem in your hometown.
Notice that these problems are not complete. There are no statistics given so we cannot actually work them out. What we can do is choose which inference procedure(s) would be appropriate. The following task will help you organize your thoughts and help you create in developing your flow chart.
Task 2: GENERATE - Brainstorm and make Lists
Before you get to make the decisions you need to take some time to write down all of the possibilities available to you for testing and inference procedures. Remember that there are confidence intervals as well. You can use your notebook and write it down, you may open a documents or you can add post-it notes to this page: add a post-it note for each inference procedure here.
Once your have all of the inference procedures written or posted, you need to think about how to organized that list.
Your second brainstorming acitiviy will be to write down a list of questons you can ask yourself while reading throguh the problem. These questions should lead you to figure out which procedure to use. You can also add to this list the key words and phrases in the problem that can help you make a decision.
You can do this with more post-it notes, write it in your notebook or in a document.
Be sure you are saving all of these to share. Before you move on to the next TASK , you need to upload your brainstorming lists or you will be sahring with your class face to face.
Task 3: SORT and CONNECT - from lists to groups to flow chart
Here are options for the final product. Allow students to get creative in how they organize the flow chart. They are required to explain the reasoning and show how it works in the end...
Now that you have the list of possible inference procedures and a list of questions and clues, you can move forward.
Sort:
Students, sort these procedures into groups based on the clues the problems can give. You could sort by the number of samples, parameter of interest, the type of date you would be given.
Do not forget about confidence intervals, linear regrassion and Chi-Square!
You are making groups of tests you think related to each other in some way.
Connect:
Now students, you are charged with creating the flow chart. Take your groups and start conencting! Make connections. Your chart should “flow” you from the problem to the clues and questions to a testing proceudre.
Be sure to provide reasoning. What clues did you start with? why did you choose that? What was your thoguth processs as you were making these connections?
Be sure you are documenting everything, either on paper or online. Keep track of each step. So far you should have:
1. A list of inference procedures.
2. A list of questions and clues to help you connect and sort.
3. A document where you have placed the inference procedures from list 1 in gorup using the questions and clue from list 2.
4. A flow chart that has all of the elements from list 1 and 2 that will help you decide what inference procedure to use.
Next you will try out your flow chart.
Here are the "problems" from page 1 of this activity...
- A teacher wants to know if the method of instruction affects how well students learn. Using two classes of the same level of statistics, she teaches one class using lecture only and the other class using lecture and group work. She measures the level of learning by giving both classes the same test.
- A student of political science wished to determine whether there is a relationship between the gender of a student and their political affiliation.
- A student wishes to test if SUV drivers in his state are more likely to be male than female. He randomly selects 50 students from a list of registered SUV drivers and records their gender.
- Your friend in Portland claims that many drivers who pass her while she awaits the school bus are talking on a cell phone. You think it is a worse problem in your hometown.
Use your flow chart to see if you can decide which inference procedure(s) would be best. You can also try using it here: Kahn Academy Inference procedure multiple choice practice
write down your answers and draw on you flow chart the path you flowed through to asnwer each one (number the paths). take a photo of it so you can share......keep scrolling :)
scroll down for the answers
- 2 sample t-test for a difference of means
- Chi-square test of independence null: There is no association between gender and political affiliation. Alternative: There is.
- 1 sample z-test null p = .5 alt: p > .5 p = true proportion of SUV owners that are male
- 2 sample z-test for a difference in proprotions.
Task 4: ELABORATE and SHARE your flow chart
Elaborate:
First make your flow chart more useful by including details for each test that would help you to complete the iference procedure once your flow charts helps you make a decision. Include: how to write null and alternative hypothesis, what conditions to check, how to find the test statistic and how to pind the p-value.
You will now create an explanatory video and share your flow chart with the class. You can creae your video using flipgrip and share it in the CANVAS assignment. You can also upload your: lists, sort and final flow chart to the assignemtn as well.
WHAT TO INCLUDE IN THE ELABORATE:
- I want you to display the flow chart in a way that is pleasing to the eye. Create a document or presentation that you can share face to face or online with peers.
- Include a voice description answering the following questions about their flow chart: What are the questions you are asking yourself to decide what procedure to use. How did you organize your flow chart and WHY did you organized it that way?
APPLY the FLOW CHART TO PROBLEMS
Solutions:
Choosing the Correct Testing Procedure: ANSWER KEY
- Matched pairs t-test : : = true mean difference in times (m – f)
- Chi-square homogeneity of proportions : The true proportion that get ear infections is the same for all three treatments : It isn’t.
- Linear regression t-test : : = the true slope of the least squares regression line using x = years and y = salary
- 2 sample t-test : : (s = silent, r = regular)
- Chi-square goodness of fit test : the color distribution hasn’t changed. : It has.
- 1 sample t-test : = 51000 : > 51000 = true mean income in California
- 2 sample t-test : : (d = duracell, e = eveready)
- 1 sample t-test : = 38 : 38 = true mean number of contacts
- 1 sample z-test : p = .5 : p > .5 p = true proportion of students with a MySpace or Facebook page
- Linear regression t-test : : = the true slope of the least squares regression line using x = age and y = miles
- Chi-square test of independence : There is no association between type of music preferred and favorite academic subject. : There is.
- Depending on the sampling procedure, this could be several different tests. If one sample of students, then a chi-square test of independence. If one sample of iPod owners, then a one sample z test. If two samples, one of males and one of females, then a chi square homogeneity or 2 sample z test.
- 1 sample t-test : = 1 : > 1 = true mean brushing time
- Chi-square goodness of fit test : the colors are uniformly distributed : They aren’t.
- Matched pairs t-test : : = true mean difference in length (a – b)
- Chi-square homogeneity of proportions : The true proportion that get heart attacks is the same for all three treatments : It isn’t
Your final task is to apply the flow chart to the problem set below:
Include in your answers to each problem: the testing procedure you would use (be specific in naming it), the null and alternative hypothises, the parameter of interest.
HW #35: Choosing the Correct Testing Procedure: For each of the following scenarios, identify the inference procedure you would use (problems 11-20 from Daren Starnes).
- In your psychology class, your group (5 students) wants to investigate the relative intelligence of mice. You decide to perform an experiment on mice, using mazes. Each of you has one male and one female mouse at home (for a total of 10 mice), and you each build a different maze. Each of you will allow each mouse one trial and record the time to reach the cheese at the end of the maze.
- Xylitol is a food sweetener that may also have antibacterial properties. In an experiment conducted in Finland, 1 group of children regularly chewed gum with Xylitol, 1 group regularly took Xylitol lozenges, and a third group regularly chewed gum that did not contain Xylitol. The experiment lasted 3 months and researchers noted whether each child had an ear infection during that period.
- Is there a relationship between the number of years a teacher has worked and their annual salary?
- Researchers have noted that sleep deprivation leads to car accidents and other mistakes, often due to inattention or slower reaction time. In order to examine the level of sleep deprivation in high school students, a researcher performs the following study. At 10 a.m. on a particular school day, students in two classes play a computer game that is actually recording the time it takes them to negotiate a mental obstacle course. At 2 p.m. that day, one of the classes is given 30 minutes in a silent, dark room with comfortable furniture, and the students are allowed to sleep. The other class has regular classes. At 3 p.m., both classes play the computer game again. The researcher records the differences in the times it takes each student to complete the game.
- Suppose that 25% of all Hondas produced last year were white, 25% silver, 20% black, 15% blue, 10% green, and 5% other. To see if they should change the distribution of colors for cars produced next year, Honda takes a random sample of potential car buyers and asks what color they prefer the most.
- Suppose that the 2000 Census showed that the mean household income in the US was $51,000. A random sample of Californians was taken to see if Californians make more money than the rest of the country.
- Which brand of AAA batteries last longer, Duracell or Eveready?
- According to a recent survey, a typical teenager has 38 contacts stored in his/her cell phone. Is this true at your school?
- Do the majority of students at your school have a MySpace or Facebook page?
- Is there a relationship between the age of a car and the number of miles it has been driven?
- Is there a relationship between the type of music a student prefers and the student’s favorite academic subject?
- Is one gender more likely to own an iPod?
- Do students spend at least 1 minute brushing their teeth, on average?
- Are the colors uniformly distributed in Fruit Loops cereal?
- Which brand of razor gives a closer shave? To answer this question, researchers recruited 25 men to shave one side of their face with Razor A and the other side of their face with Razor B. After 12 hours the length of the men’s whiskers was measured.
- To see what factors influence heart attacks, subjects were recruited for an experiment and randomly assigned to one of three treatment groups: low fat diet, exercise, and both.