Curriculum / Math / 11th Grade / Unit 8: Probability and Statistical Inference / Lesson 5
Math
Unit 8
11th Grade
Lesson 5 of 13
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Lesson Notes
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Calculate relative frequencies in two-way tables to analyze data and determine independence.
The core standards covered in this lesson
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.
The foundational standards covered in this lesson
S.ID.B.5 — Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
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?
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.
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?
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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
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.
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..
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.
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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Use conditional probability to make decisions about medical testing.
Topic A: Probability
Determine probabilities of mutually exclusive events.
Standards
S.CP.A.1
Determine probabilities of events that are not mutually exclusive.
S.CP.A.1S.CP.B.6S.CP.B.7
Calculate conditional probabilities.
S.CP.A.3
Determine when events are independent and describe independent events using everday language.
S.CP.A.2S.CP.A.3S.CP.A.5
S.CP.A.4
S.CP.A.2S.CP.A.3
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Topic B: The Normal Distribution
Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation, and shape of a histogram.
S.IC.A.1
Derive and calculate population percentages based on a normal distribution of data.
S.IC.A.2S.IC.B.4
Use $${z-}$$scores to identify population percentiles.
S.IC.B.4
Topic C: Statistical Inferences and Conclusions
Describe and compare statistical study methods.
S.IC.B.3S.IC.B.6
Use multiple random samples to estimate a population mean or proportion and verify the validity of the sampling method by analyzing the means and standard errors of samples.
Calculate and describe the margin of error in context and use larger sample sizes to minimize the margin of error.
Compare two treatments in experimental data and determine if the difference between the two treatments is significant.
S.IC.B.5
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