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23rd April

23rd April: Inferential Statistics - Confidence intervals and hypothesis testing

Learning Outcomes

Students working at OL should be able to

  • Recognise the concept of a hypothesis test
  • Calculate the margin of error for a population proportion
  • Conduct a hypothesis test on a population proportion using the margin of error

Students working at HL should be able to

  • Build on the concept of margin of error and understand that increased confidence level implies wider intervals.
  • Use sampling distributions as the basis for informal inference
  • Perform univariate large sample tests of the population mean (two-tailed z-test only)
  • Use and interpret p-values

 

 

Analysing Interpreting and Drawing Inferences from Data
SEC Exam Questions
Geogebra Files
Explanatory Videos

Inferential Statistics

https://www.scoilnet.ieuploads/resources/32151/31893.pptx Added: 26 Mar 2020 Contributor: PDST Resource type: Presentation

This content comprised material deferred during the introduction of the new project maths syllabus – namely inferential statistics. Topics visited included sampling variability, the relationships between a population and a sample and hypothesis testing

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Presentation for use in class to explore inferential statistics.

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Inferential Statistics for Proportions - Plan

https://www.scoilnet.ieuploads/resources/29914/29650.pdf Added: 25 Jun 2019 Contributor: PDST Resource type: Lesson Plan

This Teaching and Learning plan helps students understand why sampling is important, to identify that there is a link between statistics and probability. To understand the phrase “inferential statistics” and to understand the link between the 95% confidence and the empirical rule. They also recognise how sampling variability influences the use of sample information to make statements about the population.

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: To introduce students to inferential statistics for proportions.

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Project Maths Workshop 10 Notes

https://www.scoilnet.ieuploads/resources/32399/32141.pdf Added: 31 Mar 2020 Contributor: PDST Resource type: Guide/notes

Workshop 10 focused on the importance of using a variety of approaches and strategies when teaching and learning mathematics.Time was spent discussing inferential statistics and in particular deferred material which will be examined for Leaving Cert. 2015. Activities on problem-solving and an overview of the process of lesson study were also gone through on the day. If you missed workshop 10 or want to go back over some of the activities done on the day, you’ll find videos of the full workshop and all the resources used or references during the workshop below.You will find all resources used in workshop 7 here including videos of the full day.

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

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Content Course 5 Inferential Statistics and Functions Booklet

https://www.scoilnet.ieuploads/resources/32157/31899.pdf Added: 26 Mar 2020 Contributor: PDST Resource type: Worksheet / Activity

This content comprised material deferred during the introduction of the new project maths syllabus – namely inferential statistics. Topics visited included sampling variability, the relationships between a population and a sample and hypothesis testing.

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Booklet for use in class to assess students understanding of inferential statistics.

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SEC 2019 HL Paper 2 Question 8 - Inferential Statistics

https://www.scoilnet.ieuploads/resources/32167/31909.pdf Added: 26 Mar 2020 Contributor: PDST Resource type: Assessment / Exam Papers

SEC past exam question on inferential statistics with a part on the normal distribution

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: SEC past exam question to assess student understanding of sampling and z- scores

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2019 Paper 2 Ordinary level Question 8 b

https://www.scoilnet.ieuploads/resources/32685/32427.pdf Added: 22 Apr 2020 Contributor: PDST Resource type: Exam Papers

ordinary level exam paper question on inferential statistics

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Assessment

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2018 Higher level paper 2 Question 8

https://www.scoilnet.ieuploads/resources/32686/32428.pdf Added: 22 Apr 2020 Contributor: PDST Resource type: Exam Papers

Exam paper question on inferential statistics

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Assessment

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2018 Paper 2 Ordinary level Question 9 b

https://www.scoilnet.ieuploads/resources/32687/32429.pdf Added: 22 Apr 2020 Contributor: PDST Resource type: Exam Papers

Exam paper question on inferential statistics

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Assessment

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Understanding the sampling distribution of a proportion

https://www.geogebra.org/m/Dn5ecvfq Added: 22 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation / Tool

Understanding the sampling distribution of a proportion

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Use in conjunction with the mobile-phone locations activity from the workshop 10 teacher resource booklet.

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Distribution of sample means

https://www.geogebra.org/m/AIWxIWpT Added: 22 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation

This interactive simulation gives a representation of the distribution of sample means from a large population

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: This is a visual aid to enhance student understanding of the distribution of sample mean.

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Sampling distributions from a skewed population

https://www.geogebra.org/m/KgDJKxmo Added: 22 Apr 2020 Contributor: PDST Resource type: Demonstration / Simulation

This interactive simulation gives a representation of the distribution of sample means from a large skewed population

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: This is a visual aid to enhance student understanding of the distribution of sample means from a skewed population

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Margin of Error and Confidence Intervals HL

https://youtu.be/fD3B22vd300 Added: 23 Apr 2020 Contributor: PDST Resource type: Audio / Video

Margin of error and confidence levels, suitable for ordinary level up to 5 mins.

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Demonstration of the margin of error for a population proportion and confidence intervals

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Confidence interval for the mean

https://youtu.be/MzjmDGjGomE Added: 23 Apr 2020 Contributor: PDST Resource type: Audio / Video

video demonstration of the confidence interval for the mean of a population

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Video demonstration creating a confidence interval for the mean of a population.

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Hypothesis testing

https://youtu.be/qAzRBNK9xKU Added: 23 Apr 2020 Contributor: PDST Resource type: Demonstration

Video demonstration on Hypothesis testing

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Suitable for leaving certificate inferential statistics.

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Hypothesis test population proportion example

https://youtu.be/dZPAvPMGtTU Added: 23 Apr 2020 Contributor: PDST Resource type:

Example question from 2014 Higher level paper 2 Question 8(b) on hypothesis testing.

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: Leaving cert inferential statistics

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Hypothesis test population mean example

https://youtu.be/Rt6BLHsSJxE Added: 23 Apr 2020 Contributor: PDST Resource type: Demonstration

Leaving cert higher level 2015 exam paper 2 Question 2 (b)

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Mathematics

Strand: 1. Statistics & Probability

Strand unit: 7. Data: Analyse, Interpret, Draw Conclusions

Suggestions for use: leaving cert Inferential statistics

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