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Mathematical Practices: Surveys, Experiments, and Observational Studies

Learn how to determine whether a situation calls for a survey, experiment, or observational study. Explore examples and design simulations to analyze data and make inferences.

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Mathematical Practices: Surveys, Experiments, and Observational Studies

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  1. Five-Minute Check (over Lesson 8–1) Mathematical Practices Then/Now New Vocabulary Example 1: Real world Example: Design a Simulation Example 2: Design a Simulation by Using Random Numbers Example 3: Conduct and Evaluate a Simulation Example 4: Conduct and Summarize Data from a Simulation Lesson Menu

  2. Determine whether the situation calls for a survey, an experiment, or an observational study. Explain.MOVIES A production studio played a movie for a test audience and watched their reactions. A.Survey; members of the sample are observed and asked their opinions. B.Experiment; members of the sample are observed and affected by the study. C.Observational study; members of the sample are observed and unaffected by the study. D. Experiment; members of the sample are treated and affected by the study. 5-Minute Check 1

  3. Determine whether the situation calls for a survey, an experiment, or an observational study. Explain.AUTHORS At a library, every 10th person is asked some questions about their favorite author. A.Survey; members of the sample are observed and unaffected by the study. B.Survey; members of the sample are asked for their opinions. C.Observational study; members of the sample are observed and unaffected by the study. D. Experiment; members of the sample are treated and affected by the study. 5-Minute Check 2

  4. TELEVISION The management of a detention center alters the colors of their walls then compares the behaviors of their kids with the kids where the colors were not changed. Determine whether the situation describes a survey, an observational study, or an experiment. Explain your reasoning. A.observational study; the kids are unaffected by the study B.observational study; the kids are affected by the study C.experiment; the kids are divided into two groups where one group is affected by the study D.experiment; the kids are divided into two groups but neither group is affected by the study 5-Minute Check 5

  5. COLLEGE Mariana surveyed a random sample of 20% of the senior class about their college plans. She found that 18 seniors planned to go to an out-of-state college. What is the most reasonable inference about the number of seniors s in the school who plan to go to an out-of-state college? A.s = 36 B. s = 90 C. s = 180 D. s = 360 5-Minute Check 5

  6. Mathematical Practices 1Make sense of problems. 2Reason abstractly and quantitatively. 3Construct viable arguments. 4Model with mathematics. Content Standards S.IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. S.IC.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. MP

  7. You calculated simple probability. • Collect and analyze data by conducting simulations of real-life situations. • Use data to compare theoretical and experimental probabilities. Then/Now

  8. simulation • probability model • theoretical probability • experimental probability • relative frequency Vocabulary

  9. Example 1 Design a Simulation SOFTBALL Mandy is a pitcher on the softball team. Last season, 70% of her pitches were strikes. Design a simulation to estimate the probability that Mandy’s next pitch is a strike. Step 1There are two possible outcomes: strike and no strike (a ball). Use Mandy’s expectation of strikes to calculate the theoretical probability of each outcome.

  10. Example 1 Design a Simulation Step 2We can use the random number generator on a graphing calculator. Assign the integers 1-10 to accurately represent the probability data. Step 3A trial will represent one pitch. The simulation can consist of any number of trials. We will use 50.

  11. Example 1 SCHOOL BUS Larry’s bus is late 60% of the time. Design a simulation that can be used to estimate the probability that his bus is late. A.Use a random number generator for 50 trials with integers 1 through 10. 1-6: the bus is late; 7-10: the bus is not late. B.Use a random number generator for 50 trials with integers 1 through 10. 1-6: the bus is not late; 7-10: the bus is late. C.Flip a coin for 50 trials. heads: the bus is late; tails: the bus is not late. D.Roll a die for 50 trials. 1-4: the bus is late; 5-6: the bus is not late.

  12. Example 2 Step 1Possible Outcomes Theoretical ProbabilityCheese 30%Pepperoni 30%Peppers and onions 20%Sausage 20% Design a Simulation by Using Random Numbers PIZZA A survey of Longmeadow High School students found that 30% preferred cheese pizza, 30% preferred pepperoni, 20% preferred peppers and onions, and 20% preferred sausage. Design a simulation that can be used to estimate the probability that a Longmeadow High School student prefers each of these choices.

  13. Example 2 Design a Simulation by Using Random Numbers Step 2 We assume a student’s preferred pizza type will fall into one of these four categories. Step 3 Use the random number generator on your calculator. Assign the ten integers 0–9 to accurately represent the probability data. The actual numbers chosen to represent the outcomes do not matter. Outcome Represented byCheese 0, 1, 2Pepperoni 3, 4, 5Peppers and onions 6, 7Sausage 8, 9

  14. Example 2 Design a Simulation by Using Random Numbers Step 4 A trial will consist of selecting a student at random and recording his or her pizza preference. The simulation will consist of 20 trials.

  15. Example 2 PETS A survey of Mountain Ridge High School students found that 20% wanted fish as pets, 40% wanted a dog, 30% wanted a cat, and 10% wanted a turtle. Which assignment of the ten integers 0–9 accurately reflects this data for a random number simulation? A. Fish: 0, 1, 2 B. Fish: 0, 1Dog: 3, 4, 5, 6 Dog: 2, 3, 4, 5Cat: 7, 8 Cat: 6, 7Turtle: 9 Turtle: 8, 9 C. Fish: 0, 1 D. Fish: 0, 1Dog: 2, 3, 4, 5, 6 Dog: 2, 3, 4, 5Cat: 7, 8 Cat: 6, 7, 8Turtle: 9 Turtle: 9

  16. Example 3 Conduct and Evaluate a Simulation SOFTBALL Mandy is a pitcher on her high school softball team. Last season, 70% of her pitches were strikes. Conduct the simulation that can be used to estimate the probability that Mandy’s next pitch is a strike.

  17. Example 3 Press and select [randInt (].Then press 1 , 10 , 50 ) ENTER . Use the left and right arrow buttons to view the results. Make a frequency table and record the results. Conduct and Evaluate a Simulation

  18. Example 3 Conduct and Evaluate a Simulation Calculate the experimental probabilities. Answer:

  19. Example 3 SCHOOL BUS Larry’s bus is late 60% of the time. Conduct a simulation that can be used to estimate the probability that his bus is late.

  20. Example 4 Conduct and Summarize Data from a Simulation SOCCERLast season, Yao made 18% of his free kicks. Conduct a simulation using 50 trials and report the results, using appropriate numerical and graphical summaries. Compare the experimental and theoretical probabilities.

  21. Example 4 Conduct and Summarize Data from a Simulation Answer: Answers will vary, but should include a frequency table from the simulation and the corresponding bar graph. Sample answer: P(Made Kick) = 22%, P(Missed Kick) = 78%. The experimental probability is very close to the theoretical probability of 18%.

  22. Example 4 Conduct and Summarize Data from a Simulation Answer: Answers will vary, but should include a frequency table from the simulation and the corresponding bar graph. Sample answer: P(Made Kick) = 22%, P(Missed Kick) = 78%. The experimental probability is very close to the theoretical probability of 18%.

  23. Example 4 Which one of these statements is not true about conducting a simulation to find probability? A.The experimental probability and the theoretical probability do not have to be equal probabilities. B.The more trials executed, generally the closer the experimental probability will be to the theoretical probability. C.Previous trials have an effect on the possible outcomes of future trials. D.Theoretical probability can be calculated without carrying out experimental trials.

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