Download Binomial Test and Probability

Binomial Test and Probability Objectives: •
Students know the importance of statistics in scientific research After completing this activity the students will be able to: •
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Calculate the P value for a binomial test using Excel. Either accept or reject the null hypothesis based on the p‐value. Standards: Investigation & Experimentation ‐ Grades 9 To 12 1.Scientific progress is made by asking meaningful questions and conducting careful investigations. As a basis for understanding this concept and addressing the content in the other four strands, students should develop their own questions and perform investigations. Students will: a. Select and use appropriate tools and technology (such as computer‐linked probes, spreadsheets, and graphing calculators) to perform tests, collect data, analyze relationships, and display data. b. Recognize the issues of statistical variability and the need for controlled tests. Probability and Statistics‐ Grades 8‐12 1. 0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces. 2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces. 3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses. 4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families. Materials: Binomial Test PowerPoint Pennies for each student pair and scotch tape Paperclips or other small objects used for making trick coins for each pair Binomial Test and Probability Notes Binomial Test and Probability Activity Worksheet Bee Results and Conclusion Handout Computer with Excel Instructional Breakdown: Time 10 minutes Activity Warm‐Up Engage 25 minutes Lecture and Note Taking Explain Teacher Action Teacher passes out note taking guide and directs students to complete the warm‐up: • What is a hypothesis? • What is a prediction? • What is the difference between a hypothesis and a prediction? Warm up also appears on PowerPoint Once students have completed the warm‐up, teacher asks students to share responses. Teacher then defines null hypothesis, when an outcome is explained by chance. Teacher gives a brief introduction to the importance of good statistics in science. Statistics is an extension of probability theory, so instead of talking about probability and bees, let’s start with the probability of coins… What are the odds that you flip a coin and get tails? What are the odds that you flip a coin twice and get 2 tails? What’s are the odds that you flip a coin two times and get one tail and one head? What are the odds that you flip a coin twice and get 2 tails? What are the odds that you flip a coin two times and get one tail and one head? What are the odds that you flip a coin 20 times and get 14 heads or more? Teacher shows probability distribution Teacher defines binomial test, which is an exact test of the statistical significance of deviations from a theoretically expected distribution of observations into two categories. The most common usage is in a situation where there are two kinds of outcomes. Teacher explains how to calculate a binomial test in Excel and shows in an Excel spreadsheet. P = which is the percent chance that our result could have occurred by random. Student Action Students complete warm up on their notes and then share out answers with whole class. Students write down a definition for null hypothesis in their notes. Students respond to questions Students write down the probability equations for flipping coins in their notes. Students write a definition for binomial test in notes. Students write down the question that we are using the binomial test to answer. Students write down a definition for P and when you accept and reject the null hypothesis. Students respond to question 20 minutes Coin Activity Explore 15 minutes Example of How to Analyze Bee Data Elaborate 20 minutes Analyzing their Own Bee Data Evaluate 35 minutes Results and conclusion sections of paper Evaluate When P is < 0.05, we reject the null hypothesis. What do we conclude when P = .057? How does this relate to bees? Teacher passes out coins, scotch tape, paperclips, computers, and activity handouts. Teacher first asks students to log onto computers and open Excel. Then teacher explains that the goal is to make the best trick coin. Once you make your trick coin, make a prediction of what you think your results will be of flipping your coin? Then begin flipping your coin and recording your results. When you are finished, move onto the conclusion questions. Teacher circulates to help students create their fake coin, record results, calculate P, and analyze their results. When students are finished, teacher asks them to share out who had the best trick coin and what their statistical evidence was for that. Teacher directs students to start working on part 2 of the activity: an example of analyzing bee data. Teacher circulates to help students Teacher asks for students to share results. Teacher uses PowerPoint to show results Teacher directs students to now work on their own data by following the instructions on their handout in part 3. Teacher helps students use Excel, create bar graphs, and make calculations Teacher gives students the handout and PowerPoint to explain what to include in the results and conclusion section of their paper. What should be in Results section: • Have at least one table or figure. • Title your tables and figures • Do not include a table and figure of the Students, using a coin, scotch tape and any small piece of material they can find, alter the tail side of the coin. Students make a prediction for how many times heads will come up, if they toss the coin 20 times. Students share out their predictions. Students flip the coin and record results in a table. Students write a short analysis of their results. Did their results match their prediction? Students use Excel to find P, the percent chance that the outcome occurred randomly. Then explain what their P value means Students explain why they think their trick coin is the best based on their competing p values. Students work on example problem. Students share out results Students enter their data from their lab notebooks in Excel in a table, make a bar graph of their data, then calculate their p value. Students then repeat this process collating the data for all groups that worked on the same question Students begin adding their statistical data to their results and conclusion section. 5 minutes same data • Include statistics. • Explain your tables/figures in words • Refer to your figures by number. What to include in Conclusion section: • What do your results mean? Compare to hypothesis and prediction. • Why do you think you got what you did? • Explain what you might do differently next time. Teacher then explains that this is your time to work with your group members on a draft for both sections of your paper. Teacher circulates to help students write their results and conclusion. Teacher reminds students to save, share with group members and log off computers. Conclusion A binomial test is a statistical test that allows us to calculate the deviations observes from what was expected You calculate a binomial test in Excel by: =BINOMDIST(6, 20, 0.5, TRUE) P is the percent chance that what happened occurred randomly. Generally, when P < .05 we reject the null hypothesis A null hypothesis is that the outcome is explained by chance. When finished, students save and share their work and log off of the computers. Name : ___________________________________Date: _________________________Class: __________________ Binomial Test and Probability Notes Warm Up: 1. What is a hypothesis? 2. What is a prediction? 3. What is the difference between a hypothesis and a prediction? Null Hypothesis (H0): Probability Equations: Binomial Test: Calculating the binomial test in Excel: Our Question: =BINOMDIST(6, 20, 0.5, TRUE). 6 = the number of times it is tails, 20‐14= 6. 20 = the number of times you flipped the coin. 0.5 = the expected probability of getting heads TRUE = calculating the sum of the probabilities of the observed number and all more extreme values (14 +15 + 16 + 17 +18 +19 +20) P: Generally, when P is < 0.05, we reject the null hypothesis. When P is >0.05 we ____________________the null hypothesis. Name : ___________________________________Date: _________________________Class: __________________ Binomial Test and Probability Activity Introduction: In this activity you will learn how to do a binomial test, a statistical test that allows us to calculate the deviations observed from what was expected. You will learn how to calculate a binomial test in Excel, and how to calculate the P value, the percent chance that what happened occurred randomly. In this way, you will be able to tell whether or not your outcome was due to chance, a null hypothesis (H0), or happened because something else was changing the outcome. Materials: Pennies for each student pair Scotch tape Student Handout Computer with Excel PART 1: COIN TOSS EXPERIMENTS EXPERIMENT 1: Take the tail side of your coin and alter it with scotch tape and some piece of material. Now make a prediction as to how many times heads will come up if you toss the coin 20 times. PREDICTION: ___________________________________________________________________________________ ___________________________________________________________________________________ ___________________________________________________________________________________ Collect data: Record each time that your coin lands on heads or tails. Make big high flips! Table 1: Heads or Tails in a Coin Toss (n=20) Toss 1 Heads Tails Toss 11 Heads Tails Toss 2 Toss 3 Toss 4 Toss 5 Toss 6 Toss 7 Toss 8 Toss 9 Toss 10 Toss 12 Toss 13 Toss 14 Toss 15 Toss 16 Toss 17 Toss 18 Toss 19 Toss 20 Total QUESTIONS: 1. Did your results match your prediction? Why or why not? ___________________________________________________________________________________ ___________________________________________________________________________________ 2. Write a equation that you could enter into Excel to calculate the P value of the binomial test: P =BINOMDIST(_______, _________, _______, TRUE) 2. Now calculate P, the percent chance that what occurred happened randomly, using Excel. P = 3. Is P greater than or less than 0.05? 4. Would you accept or reject the null hypothesis? ______________________________________________ 5. What does it mean to accept the null hypothesis? ____________________________________________ _____________________________________________________________________________________. What does it mean to reject the null hypothesis? _____________________________________________ _____________________________________________________________________________________. 6. If you were given only the results, without seeing the coin itself, what would you conclude about the coin: is it fair or not? Explain. ____________________________________________________________________________________ _____________________________________________________________________________________ PART 2: BEE EXPERIMENTS EXPERIMENT 1: Two dishes with sugar water were placed 10 meters from a bee hive. Both dishes were the same, except one dish, the experimental dish, had a bee predator glued to it, while the other, the control dish, did not. More bees landed on the control dish than the experimental dish. Below is the data collected from the experiment: Table 3: Number of Bees Landing on the Experimental and Control Sugar Dishes Dish Control Experiment Total Number of Bees Landed 21 8 29 1. What is the question that you are asking? _____________________________________________________ ___________________________________________________________________________________________ 2. Write a equation that you could enter into Excel to calculate the P value of the binomial test: P =BINOMDIST(_______, _________, _______, TRUE) 3. Calculate your P value by entering your equation into Excel P = _____________ 4. Do you accept or reject the null hypothesis? Why? Show your work. ___________________________________________________________________________________ ___________________________________________________________________________________ 5. Explain what accepting or rejecting the null hypothesis means in the case of the bee experiments. ___________________________________________________________________________________ ___________________________________________________________________________________ 6. Why would scientists design experiments, so that they are binomial in nature? ___________________________________________________________________________________ __________________________________________________________________________________ PART 3: ANALYZING YOUR OWN DATA Open a new Excel Document and title them your “group name bee results”. 1. Add up all your bees landing on your control and experimental dishes, Create a table. You can analyze bees and wasps together and/or separately. e.g. Table 1: Number of Bees Landing on the Experimental and Control Sugar Dishes Dish Control Experiment Total Number of Bees Landed 21 8 29 2. Make a bar graph of your results. 3. Calculate your P value. 4. Gather data from other groups that tested the same thing and copy their data into your results. Add the results together, as in the example below… Dish Control Experiment Total Exp 1: Number of Bees Landed 21 8 29 Exp 2: Number of Bees Landed 4 3 7 Total 25 11 36 4. Calculate P for all the groups combined that did the same experiment. Does your result change? How do you interpret these combined results (could have the different groups have done things differently)?