Nuffield Mathematics teaching resources are for use in secondary and further education

FSMQ Level 3 (pilot) Hypothesis testing scheme of work

Note: AQA have decided to discontinue this FSMQ. The last exam will be in the June 2018 series, with a final re-sit opportunity in 2019.

Before starting this Advanced (Level 3) FSMQ students should have acquired the skills and knowledge associated with the Statistics assessment objective of GCSE Mathematics or with an Intermediate (Level 2) FSMQ in Data, or equivalent.

A suggested work scheme showing topic areas and methods to be covered is given below.  The order and time allocations can be varied to suit different groups of students. 

Note that the Nuffield assignments below will not contribute to the AQA assessment of this FSMQ which is by examination only. Many of the resources below were written for the legacy FSMQ ‘Using and applying statistics’. The content of this AQA pilot FSMQ ‘Hypothesis testing’ is very different. Although the data included in these resources may be useful, you will need to adapt the activities to match the content of this FSMQ. You should disregard any information about portfolio work.

Topic area

Content

Nuffield resources 
The links below go to pages from which you can download the resources, some recently revised.

Most were originally written for earlier FSMQs and are likely to need adapting for use with this unit.

Probability laws
(6 hours)

Revise basic probability methods.

Multiplication law for probabilities of independent events

Addition law for probabilities of exclusive events

Tree diagrams (for independent events only).

 

Probability  
Presentation illustrating basic methods and examples for learners to try.

Sports injuries   
Discuss the use of real data (gives age and gender, also included on spreadsheet.)

Laws of probability  
Presentation, hand-out and examples for learners to try.

Binomial distribution
(6 hours)

The use of discrete theoretical probability distributions to model populations.

Binomial probabilities using notation \begin{pmatrix} n \\ r \end{pmatrix} p^rq^n^-^r

Histograms   
Instructions explaining how to construct an accurate histogram and frequency polygon in Excel.

The normal distribution
(10 hours)

The use of continuous theoretical probability distributions to model populations.

Features of a normal distribution, including:

· continuous data

· symmetry

· approximately two-thirds of the distribution lying within one standard deviation of the mean

· approximately 95% of the distribution lying within two standard deviations of the mean

The standard normal distribution with mean 0 and standard deviation 1.

Use of tables to find probabilities and expected frequencies.

Use of tables in reverse calculations.

Normal approximation to the Binomial Distribution.

Stature  
Data sheet gives the heights of samples of men and women from 8 countries. Student worksheet leads to main features of samples from normal distributions. Optional use of spreadsheet.

Pulse rates   
Experiment to find the effect of exercise on pulse rates.  Spreadsheet gives results from such an experiment carried out over a number of years by Dr Richard Wilson at the University of Queensland.

Casio calculators      
Instructions for using a Casio fx83WA or fx85WA to find the mean and standard deviation. 

Graphic calculators    
Presentation introducing students to the Casio fx-7400G PLUS calculator. 

 

Topic area

Content

Nuffield resources
The links below go to pages from which you can download the resources, some recently revised.
Most were originally written for earlier FSMQs and likely to need adapting for use with this unit.

Sampling
(8 hours)

Sampling from a parent population

Precision and sample size. Include discussion of the cost in both time and money of improving accuracy by removing bias and increasing sample size.

Distribution of the sample mean and sample proportion from a normal population.

Confidence intervals.

Parking permits   
Presentation, activity, information sheet and work sheet including finding random and representative samples, questionnaire design etc.

DISCUSS Sampling   
Simulations to aid understanding of how variation occurs within and between samples.  Internet access needed.

Hypothesis testing
(12 hours)

Null and alternative hypotheses

One-tail and two-tail tests (binomial and normal distributions only)

Significance level and critical region

Specific tests including opinion polls, food tasting (including triangle test and pairs difference test)

Clinical trials including placebo and double-blind trials

 

Rain or shine 
Students use sunshine and rainfall data to carry out significance tests on the difference between sample means.  As part of this activity students use either a calculator or a spreadsheet to calculate mean and standard deviation values.

Gender differences
Students carry out significance tests on means in order to test hypotheses about the body measurements of boys and girls at different ages.

Music and work 
Worksheet requiring students to write an hypothesis and design an experiment to test whether listening to music has any effect on the performance of people doing work. Also includes arithmetic tests that may be used to carry out such an experiment.

Successful HE applicants 
Students carry out significance tests on proportions to test hypotheses about successful applicants to higher education. 

Election results  – data may be useful  
Spreadsheet containing the 2005 and 2010 General Election results.

Can they tell the difference? - Students use a triangle test to decide whether or not people can tell the difference between a product and a healthier alternative.

Non-parametric tests
(10 hours)

The sign test

 

The Mann-Whitney U test

 

Subject results  – data may be useful  
Spreadsheet containing A-level results in 13 subjects.

Module results – data may be useful  
Results for two modules.

Mammals  – data may be useful  
Data sheets giving body mass, brain mass, sleep duration, life span, gestation time and danger index for small, medium and large mammals.

Health data – data may be useful   
Data sets involving the health of adults and children in the UK and information about hospital waiting lists, and so on.

 

 Revision
(8 hours)

Revise topics.  Work through revision questions and practice papers.

Discuss the data sheet - make up & work through questions based on it.

 


 

Page last updated on 02 August 2017