Probability and Statistical Inference

Lesson 10

Math

Unit 8

11th Grade

Lesson 10 of 13

Objective


Describe and compare statistical study methods.

Common Core Standards


Core Standards

  • S.IC.B.3 — Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
  • S.IC.B.6 — Evaluate reports based on data.

Foundational Standards

  • 7.SP.A.1

Criteria for Success


  1. Define a parameter as a characteristic of a population that one is interested in. 
  2. Describe that an experiment is when a “treatment” is assigned to some subjects and not to others for the purpose of seeing what effect the treatments may have on a sample or population. 
  3. Describe that an observational study records data when an independent variable is not directly manipulated. 
  4. Describe that a sample survey is a type of observational study where the data is collected by asking people to respond to a set of questions about a population characteristic. 
  5. Describe that random selection when using an observational study and survey is important to the validity of the data collected and that random assignment of treatment and control is important to the validity of the data in an experiment. 
  6. Describe that because there are multiple factors that may contribute to a parameter, sample surveys and observational studies cannot determine causality, only correlation.
  7. Describe good and bad characteristics of a study design along with potential implications of those design choices.

Tips for Teachers


  • This is a pretty text-heavy lesson; however, it is very important for students to understand the idea that the strength of the statistical analysis is based on how the data was collected. If there is bias in the method of collection of data, then the statistical analysis is invalid (like the saying “garbage in, garbage out”). 
  • If there is an opportunity to introduce the idea of multiple samples, repeatedly drawn of similar sizes being used to collect information, this would help student understanding of lesson 11.
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Anchor Problems


Problem 1

You would like to know whether the number of minutes that a train is delayed correlates to the number of violent acts that occur on the platform or in the train. 

Which would result in the most reliable data? 

  1. Delay trains, on purpose, by 5 minutes, 10 minutes, and 20 minutes and track the number of violent acts reported to the MBTA police. Compare this information to when the trains are not delayed. 
  2. Use data about delayed trains and look at the report data for the MBTA police—connecting the times of each. 
  3. Ask a sample of ridership about number of violent acts witnessed and ask respondents to identify the station and the approximate time these acts took place. 
  4. Which of these is an observational study, which is a survey, and which is an experiment? How do you know?

Guiding Questions

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Problem 2

To determine if higher speed limits cause more traffic fatalities, researchers compared the number of traffic deaths on randomly selected stretches of highway within 65 mph speed limits to the number of traffic deaths on an equal number of randomly selected stretches of highway with 75 mph speed limits.

Guiding Questions

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References

Mathematics Vision Project: Secondary Mathematics Three Module 8: Statistics (Teacher Notes)Lesson 8.6, #2e (p. 34)

Module 8: Statistics (Teacher Notes) in Secondary Mathematics Three: Integrated Pathway CCSS made available by Mathematics Vision Project et al. in partnership with the Utah State Office of Education under the CC BY-NC-SA 3.0 license. © 2014 Utah State Office of Education. Accessed June 5, 2018, 2:56 p.m..

Problem 3

For each part below, determine 1) if the type of study described is a survey, observational study, or experimental study, and 2) if the study is good or bad, and why. 

  1. Why are students missing so much school in the district? A district administrator selects 300 student names at random from the enrollment list and sends a letter to each student’s home. The letter includes a page to be returned to their school signed by a parent or guardian. The page asks, “How many days has your student missed school this year?” and “What are the reasons for missing school on those days?”
  2. Why are students missing so much school in the district? A district administrator chooses one of the elementary schools in the district and asks the principal to provide information about the number of absences and the excuse notes provided to the school.
  3. Do voters in the district favor a sales tax increase of 1% to fund the parks and recreation department? A politician sends a letter to 300 voters in the district asking, “Would you pay extra money on your essential groceries to hire more government workers to plant flowers around the town?”
  4. Do voters in the district favor a sales tax increase of 1% to fund the parks and recreation department? A politician sends a letter to 300 voters selected at random in the district asking, “Would you be in favor of a 1% increase in sales tax to fund the parks and recreation department in town?”

Guiding Questions

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References

Illustrative Mathematics Algebra 2 Unit 7 Lesson 1 Being Skeptical1.2 Take Turns: Statistical Design

Algebra 2 Unit 7 Lesson 1 Being Skeptical, accessed on Feb. 12, 2021, 4:35 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Target Task


Is each of the following an observational study or an experiment? Explain your answer. 

If it is an experiment, identify the treatment variable and the response variable in the context of the problem. If it is an observational study, identify the population of interest. 

  1. A study is done to see how high soda will erupt when mint candies are dropped into two-liter bottles of soda. You want to compare one mint candy, five minute candies, and ten mint candies. You design a cylindrical mechanism that drops the desired number of mint candies all at once. You have 15 bottles of soda to use. You randomly assign five bottles into which you drop one candy, five into which you drop five candies, and five into which you drop ten candies. For each bottle, you record the height of the eruption created after the candies are dropped into it. 
  2. You want to see if fifth-grade boys or fifth-grade girls are faster at solving Ken-Ken puzzles. You randomly select twenty fifth-grade boys and twenty fifth-grade girls from fifth graders in your school district. You time and record how long it takes each student to solve the same Ken-Ken puzzle correctly. 

References

EngageNY Mathematics Algebra II > Module 4 > Topic C > Lesson 12Exit Ticket

Algebra II > Module 4 > Topic C > Lesson 12 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

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Lesson 9

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Lesson 11

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Probability

Topic B: The Normal Distribution

Topic C: Statistical Inferences and Conclusions

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