School level

# 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

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

SC Mathematics

#### How it maps to the curriculum

SC
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.

Asset type: Presentation
Language: English
Special Needs:

### Inferential Statistics for Proportions - 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.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

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

Asset type: Document
Language: English
Rights: Attribution-Noncommercial Share Alike Creative Commons
Special Needs:

### Project Maths Workshop 10 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.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

Strand unit: 2. Concept of Probability

Asset type: Document
Special Needs:

### 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.

SC Mathematics

#### How it maps to the curriculum

SC
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.

Asset type: Document
Language: English
Special Needs:

### 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

SC Mathematics

#### How it maps to the curriculum

SC
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

Asset type: Document
Language: English
Special Needs:

### 2019 Paper 2 Ordinary level Question 8 b

ordinary level exam paper question on inferential statistics

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

Suggestions for use: Assessment

Asset type: Document
Language: English
Special Needs:

### 2018 Higher level paper 2 Question 8

Exam paper question on inferential statistics

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

Suggestions for use: Assessment

Asset type: Document
Language: English
Special Needs:

### 2018 Paper 2 Ordinary level Question 9 b

Exam paper question on inferential statistics

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

Suggestions for use: Assessment

Asset type: Document
Language: English
Special Needs:

### 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

SC Mathematics

#### How it maps to the curriculum

SC
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.

Asset type: App
Language: English
Special Needs:

### 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

SC Mathematics

#### How it maps to the curriculum

SC
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.

Asset type: App
Language: English
Special Needs:

### 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

SC Mathematics

#### How it maps to the curriculum

SC
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

Asset type: App
Language: English
Special Needs:

### 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.

SC Mathematics

#### How it maps to the curriculum

SC
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

Asset type: Video
Language: English
Special Needs:

### 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

SC Mathematics

#### How it maps to the curriculum

SC
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.

Asset type: Video
Language: English
Special Needs:

### Hypothesis testing

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

Video demonstration on Hypothesis testing

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

Suggestions for use: Suitable for leaving certificate inferential statistics.

Asset type: Video
Language: English
Special Needs:

### 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.

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

Suggestions for use: Leaving cert inferential statistics

Asset type: Video
Language: English
Special Needs:

### 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)

SC Mathematics

#### How it maps to the curriculum

SC
Mathematics

Strand: 1. Statistics & Probability

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

Suggestions for use: leaving cert Inferential statistics

Asset type: Video
Language: English
Special Needs:

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