Probability and Statistical Inference

Lesson 5

Math

Unit 8

11th Grade

Lesson 5 of 13

Objective


Calculate relative frequencies in two-way tables to analyze data and determine independence.

Common Core Standards


Core Standards

  • S.CP.A.4 — Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

Foundational Standards

  • S.ID.B.5
  • 7.SP.C.8

Criteria for Success


  1. Calculate relative frequencies in a two-way table. 
  2. Assess whether particular variables are independent or dependent from a two-way table. 
  3. Calculate conditional probabilities in a two-way table. 
  4. Determine an acceptable range of values to determine independence.
  5. Connect multiple representations to show the sample space of a set of variables.

Tips for Teachers


Students analyzed two-way tables in Algebra 1 and also in eighth grade, so the lift here of finding relative frequencies and determining independence shouldn’t be too bad.

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Anchor Problems


Problem 1

Each student in a random sample of seniors at a local high school participated in a survey. These students were asked to indicate their gender and their eye color. The following table summarizes the results of the survey.

Based on this data, are "blue eyes" and "male" independent variables? How do you know?

Guiding Questions

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References

Illustrative Mathematics Two-Way Tables and Probability

Two-Way Tables and Probability, accessed on June 15, 2017, 9:04 a.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.

Modified by Fishtank Learning, Inc.

Problem 2

On April 15, 1912, The Titanic struck an iceberg and rapidly sank with only 710 of her 2,204 passengers and crew surviving. Data on survival of passengers are summarize in the table below.

Choose two variables that you think are NOT independent. Test this assumption.

Choose two variables that you think ARE independent. Test this assumption.

What did you find?

Guiding Questions

Create a free account or sign in to access the Guiding Questions for this Anchor Problem.

References

Illustrative Mathematics The Titanic 1

The Titanic 1, accessed on June 15, 2017, 9:05 a.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.

Modified by Fishtank Learning, Inc.

Target Task


Problem 1

A hypothetical 1000 two-way frequency table is below.

Are the events "a randomly selected person watched the online ad" and "a randomly selected person plans to vacation in New York within the next year" independent or not independent? Justify your answer using probabilities calculated from information in the table.

References

EngageNY Mathematics Algebra II > Module 4 > Topic A > Lesson 4Exit Ticket, Question #1

Algebra II > Module 4 > Topic A > Lesson 4 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.

Problem 2

A survey conducted at a local high school indicated that 30% of students have a job during the school year. If having a job and being in the eleventh grade are not independent, what do you know about the probability that a randomly selected student who is in the eleventh grade would have a job? Justify your answer.

References

EngageNY Mathematics Algebra II > Module 4 > Topic A > Lesson 4Exit Ticket, Question #2

Algebra II > Module 4 > Topic A > Lesson 4 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..

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 4

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Lesson 6

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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