AQA 7387 SP 2017 v0 1

• Population and samples page 11• Introduction to probability distributions page 12 • Binomial distribution page 12 • Normal distribution page 13 • Correlation and linear regression page

DRAFT 7387

Specification

For teaching from September 2017 onwards

For A-level exams in 2019 onwards

Version 0.1 11 August 2016

DRAFT

DRAFT SPECIFICA

DRAFT

3.15 Hypothesis testing, significance testing, confidence

5.3 Awarding grades and reporting results 27

5.6 Access to assessment: diversity and inclusion 28

1 Introduction

1.1 Why choose AQA for A-level Statistics

A-level Statistics is a fantastic choice for students who want to know the facts behind the figures

and want to make sense of the world around us

It goes well with subjects including A-level Biology, Psychology, Geography, Business Studies and

Economics

The logical, problem-solving and numerical skills gained, are useful for many different areas of

employment; from working with a Formula One racing team on aerodynamics, to teaching or stock

market trading

A specification designed for you and your students

This new qualification retains much of the content that we know you and your students enjoy and

you’ll recognise many of the topics This means you can still use your existing resources Topics

are clearly and logically structured and include:

• numerical measures, graphs and diagrams

• binomial distribution

• correlation and linear regression

• hypothesis testing

Clear, well-structured exams, accessible for all

To enable your students to show their breadth of knowledge and understanding, we’ve created a

simple and straightforward structure and layout for our papers, using a mixture of question styles

There is one exam paper for AS and there are two exam papers for A-level Assessment remains

100% exam based

You can find out about all our Statistics qualifications at aqa.org.uk/mathematics

1.2 Support and resources to help you teach

We’ve worked with experienced teachers to provide you with a range of resources that will help

you confidently plan, teach and prepare for exams

1.2.1 Teaching resources

Visit aqa.org.uk/7387 to see all our teaching resources They include:

• sample schemes of work and lesson plans to help you plan your course with confidence

• teachers' guide that have been checked by AQA

DRAFT

1.2.2 Preparing for exams

Visit aqa.org.uk/7387 for everything you need to prepare for our exams, including:

• past papers, mark schemes and examiners’ reports

• specimen papers and mark schemes for new courses

• Exampro: a searchable bank of past AQA exam questions

• example student answers with examiner commentaries

1.2.3 Analyse your students' results with Enhanced Results Analysis

(ERA)

Find out which questions were the most challenging, how the results compare to previous years

and where your students need to improve ERA, our free online results analysis tool, will help you

see where to focus your teaching Register at aqa.org.uk/era

For information about results, including maintaining standards over time, grade boundaries and our

post-results services, visit aqa.org.uk/results

1.2.4 Keep your skills up-to-date with professional development

Wherever you are in your career, there’s always something new to learn As well as subject

specific training, we offer a range of courses to help boost your skills

• Improve your teaching skills in areas including differentiation, teaching literacy and meeting

Ofsted requirements

• Prepare for a new role with our leadership and management courses

You can attend a course at venues around the country, in your school or online – whatever suits

your needs and availability Find out more at coursesandevents.aqa.org.uk

1.2.5 Help and support

Visit our website for information, guidance, support and resources at aqa.org.uk/7387

If you'd like us to share news and information about this qualification, sign up for emails and

This draft qualification has not yet been accredited by Ofqual It is published to enable teachers to

have early sight of our proposed approach to A-level Statistics Further changes may be required

and no assurance can be given that this proposed qualification will be made available in its current

form, or that it will be accredited in time for first teaching in September 2017 and first award in

August 2018

DRAFT

• Population and samples (page 11)

• Introduction to probability distributions (page 12)

• Binomial distribution (page 12)

• Normal distribution (page 13)

• Correlation and linear regression (page 14)

• Introduction to hypothesis testing (page 15)

• Contingency tables (page 16)

• One and two sample non-parametric tests (page 16)

• Bayes’ theorem (page 17)

• Probability distributions (page 17)

• Experimental design (page 18)

• Sampling, estimates and resampling (page 18)

• Hypothesis testing, significance testing, confidence intervals and power (page 19)

• Hypothesis testing for 1 and 2 samples (page 20)

• Paired tests (page 21)

• Exponential and Poisson distributions (page 21)

• Goodness of fit (page 22)

• Analysis of variance (page 22)

• Effect size (page 23)

DRAFT

2.2 Assessments

Paper 1

What's assessed

Specification content 3.1‒3.10

How it's assessed

• Written exam: 3 hours

• 120 marks

• 50% of A-level

Questions

• Questions requiring multiple choice, short, medium and extended answers including a

Statistical Enquiry Cycle (SEC) question

Paper 2

What's assessed

Specification content 3.11‒3.21, not precluding 3.1‒3.10

How it's assessed

• Written exam: 3 hours

• 120 marks

• 50% of A-level

Questions

• Questions requiring multiple choice, short, medium and extended answers including a

Statistical Enquiry Cycle (SEC) question

DRAFT

3 Subject content

The subject content of this specification matches that set out in the Department for Education’s

Statistics GCE subject content and assessment objectives document This content is common to

all exam boards

The subject content, aims and learning outcomes, and assessment objectives sections of this

specification set out the knowledge, skills and understanding common to all GCE Statistics exams

In addition to this subject content, students should be able to recall, select and apply mathematicalformulae See Appendix 1 (page 31) and Appendix 2 (page 33) for a list of the DfE prescribed

formulae

DRAFT

3.1 Numerical measures, graphs and diagrams

• Interpret statistical diagrams including bar

charts, stem and leaf diagrams, box and

whisker plots, cumulative frequency

diagrams, histograms (with either equal or

unequal class intervals), time series and

scatter diagrams

• Know the features needed to ensure an

appropriate representation of data using

the above diagrams, and how

misrepresentation may occur

• Justify appropriate graphical

representation and comment on those

published

• Compare different data sets, using

appropriate diagrams or calculated

measures of central tendency and

spread: mean, median, mode, range,

interquartile range, percentiles, variance

and standard deviation

• Calculate measures using calculators and

manual calculation as appropriate

• Identify outliers by inspection and using

appropriate calculations

• Determine the nature of outliers in

reference to the population and original

data collection process

• Appreciate that data can be

misrepresented when used out of context

or through misleading visualisation

Students will not be required to draw or constructstatistical diagrams

Students must learn and recall the following:

• the angle in a pie chart is given by x

total × 360

• in a histogram

f requency density= class width f requency

• the formula for calculating the arithmetic meanis

x

− = ∑f x

∑f

• range ishighest value–smallest value

• Interquartile range (IQR) = Q3 – Q1 where Q1 isthe lower quartile and Q3 is the upper quartile

• Outliers lie

• below Q1–1.5(Q3 – Q1) or above Q3+1.5(Q3 –Q1), or

• outside the limits μ ± 3σStudents will be given the following informationPopulation variance = N1∑ x−μ2

Population standard deviation = N1∑ x−μ2

3.2 Probability

• Know and use language and symbols

associated with set theory in the context of

probability

• Represent and interpret probabilities using

tree diagrams, Venn diagrams and two-way

tables

• Calculate and compare probabilities: single,

independent, mutually exclusive and

conditional probabilities

• Use and apply the laws of probability to

include conditional probability

• Determine if two events are statistically

3.3 Population and samples

• Know both simple (without replacement) and

unrestricted (with replacement) random

samples

• Know how to obtain a random sample using

random numbers tables or random numbers

generated on a calculator

• Evaluate the practical application of random

and non-random sampling techniques: simple

random, systematic, cluster, judgmental and

snowball, including the use of stratification (in

proportional and disproportional ratios) prior to

sampling taking place

• Know the advantages and limitations of

sampling methods

• Make reasoned choices with reference to the

context in which the sampling is to take place

Examples include, but are not limited to: market

research, exit polls, experiments and quality

assurance

• Understand the practical constraints of

collecting unbiased data

Students should know that for a random

• every possible sample of size n must be

equally likely to occur

Students should appreciate that snowballsampling can be used to reach populationsthat are difficult to sample when using othersampling methods eg drug users

DRAFT

3.4 Introduction to probability distributions

• Know and use terms for variability: random,

discrete, continuous, dependent and

independent

• Calculate probabilities and determine

expected values, variances and standard

deviations for discrete distributions

• Use discrete random variables to model real

world situations

• Know the properties of a continuous

distribution

• Interpret graphical representations or

tabulated probabilities of characteristic

discrete random variables

• Interpret rectilinear graphical

representations of continuous distributions

Students will be expected to learn and recall theformulae for calculating the expected value andthe variance of a discrete probability distribution,namely:

• Know when a binomial model is appropriate (in

real world situations including modelling

assumptions)

• Know methods to evaluate or read probabilities

using formula and tables

• Calculate and interpret the mean and variance

Students may use calculator functions toobtain binomial probabilities and are advised

to do so Students will be given the formulaefor calculating individual binomial

3.6 Normal distribution

• Know the specific properties of the normal

distribution, and know that data from such an

underlying population would approximate to

having these properties, with different samples

showing variation

• Apply knowledge that approximately 2

3 of

observations lie within μ ± σ, and equivalent

results for 2σ and 3σ.

• Determine probabilities and unknown

parameters with a normal distribution

• Apply the normal distribution to model real world

situations

• Use the fact that the distribution of X− has a

normal distribution if X has a normal

distribution

• Use the fact that the normal distribution can be

used to approximate a binominal distribution

under particular circumstances

Students should learn and recall thatapproximately 95% of observations lie within

μ ± 2σ and approximately 99.8% ofobservations lie within μ ± 3σStudents may use calculator functions toobtain information for a normal distributiondirectly and are advised to do so

Students should learn and recall that thenormal distribution may be used toapproximate a binomial distribution when:

3.7 Correlation and linear regression

• Calculate (only using appropriate

technology ‒ calculator) and

interpret association using

Spearman’s rank correlation

coefficient or Pearson’s product

moment correlation coefficient

• Use tables to test for significance of

a correlation coefficient

• Know the appropriate conditions for

the use of each of these methods of

calculating correlation and determine

an appropriate approach to

assessing correlation in context

• Calculate (only using appropriate

technology ‒ calculator) and

interpret the coefficients for a least

squares regression line in context;

interpolation and extrapolation, and

use of residuals to evaluate the

model and identify outliers

When evaluating Spearman’s coefficient, candidates will

be expected to:

• rank both variables consistently

• rank tied values appropriately

• use a calculator to find the correlation coefficient

Students will be expected to:

• find correlation coefficients and the coefficients for aleast squares regression line directly from thecalculator

• write the equation of a least squares regression line

in the form

• y=ax+b

• interpret correlation coefficients and the coefficients

in a least squares regression line in a given context

Students will be given the following:

Coefficients for least squares regression line: least

squares regression line of y on x is y=a+bx where

3.8 Introduction to hypothesis testing

• Use and demonstrate understanding of the

terms parameter, statistic, unbiased and

standard error

• Know and use the language of statistical

hypothesis testing: null hypothesis, alternative

hypothesis, significance level, test statistic,

1-tail test, 2-1-tail test, critical value, critical region,

and acceptance region and p-value

• Know that a sample is being used to make an

inference about the population and appreciate

the need for a random sample and of the

necessary conditions

• Choose the appropriate hypothesis test to

carry out in particular circumstances

• Conduct a statistical hypothesis test for the

proportion in the binomial distribution and

interpret the results in context using exact

probabilities or, where appropriate, a normal

approximation

• Conduct a statistical hypothesis test for the

mean of a normal distribution with known or

assumed variance, from a large sample, and

interpret the results in context

• Know the importance of appropriate sampling

when using hypothesis tests and be able to

critique the conclusions drawn from rejecting

or failing to reject a null hypothesis by

considering the test performed

Students will be expected to know and usethat:

• a parameter is a numerical property of apopulation

• a statistic is a numerical property of asample and is a function only of the values

in the sample and contains no unknownparameters

In a hypothesis test on a population

proportion, candidates may use either π or p

as the parameter in their hypotheses

The test statistic for a test on a binomialproportion, using the normal distribution as anapproximation, will be given:

p−p

p1 −p n

N 0,1

DRAFT

3.9 Contingency tables

• Construct contingency tables from real data,

combining data where appropriate, and

interpret results in context

• Use a χ2 test with the appropriate number of

degrees of freedom to test for independence in

a contingency table and interpret the results of

such a test

• Know that expected frequencies must be

greater than, or equal to, 5 for a χ2 test to be

carried out and understand the requirement for

combining classes if that is not the case

The formula for a χ2test statistic will be given

∑ O i−E i2

E i Students may use either 'independent' or'associated' in their hypotheses

Students will be expected to know how to findthe number of degrees of freedom and thatquestions set will not require the use of Yates’

correction

Students must follow the rule to combineclasses when expected frequencies aresmaller than 5, and 'pooling' is permissible

Students will not be required to use Yates’

correction

3.10 One and two sample non-parametric tests

• Use sign or Wilcoxon signed-rank tests to

investigate population median in single

sample tests and also to investigate for

differences using a paired model

• Use the Wilcoxon rank-sum test to investigate

for difference between independent samples

Students will be expected to use the sign test,

or the Wilcoxon signed-rank test to:

• test the value of a single population medianbased on a single sample

• test for a difference between two populationmedians based on a sample of 'paired' data

Students will be expected to test for adifference between two population medians,based on two independent samples, using theWilcoxon rank-sum test (this is also known asthe Mann-Whitney test)

DRAFT

3.11 Bayes’ theorem

• Calculate and use conditional probabilities

to include Bayes’ theorem for up to three

events, including the use of tree diagrams

Students will be given the formula for Bayes’

theorem and will be expected to use it inproblems that involve up to three events

P Aj B = PA j × P B A j

∑i= 1

3 PA i× P B A i

3.12 Probability distributions

• Know the use and validity of distributions which

could be appropriate in a particular real world

situation: binomial, normal, Poisson and

exponential

• Evaluate the mean and variance of linear

combinations of independent random variables

through knowledge that if X i are independently

distributed μ i , σ i2 then ∑ai X i is distributed

∑ai μ i ,   ∑ai2σ i2

• Evaluate probabilities for linear combinations of

two or more independent normal distributions

and apply this knowledge to practical situations

Students will be given the following:

Poisson probability formula:

3.13 Experimental design

• Know and discuss issues involved in

experimental design: experimental error,

randomisation, replication, control and

experimental groups, and blind and double

blind trials

• Know the benefits of use of paired comparisons

and blocking to reduce experimental error

• Use completely random and randomised block

designs

Students will be expected to explain anddiscuss these concepts in a given context

3.14 Sampling, estimates and resampling

• Use and demonstrate understanding of terms

parameter, statistic, unbiased and standard

error

• Know the use of the central limit theorem in

the distribution of X− where the initial

distribution, X , is not normally distributed and

the sample is large

Students will be expected to know and usethat:

• a parameter is a numerical property of apopulation

• a statistic is a numerical property of asample and is a function of only the values

in the sample and contains no unknownparameters

Students are expected to know that:

• the central limit theorem may be used whenthe sample size (of random samples) issufficiently large (n ≥ 30)

• it is only necessary to use the central limittheorem when the underlying population isnot normally distributed

DRAFT

3.15 Hypothesis testing, significance testing, confidence

intervals and power

• Use confidence intervals for the mean using z

or t as appropriate, interpreting results in

practical contexts

• Know that a change in sample size will affect

the width of a confidence interval

• Evaluate the strength of conclusions and

misreporting of findings from hypothesis

tests, including the calculation and

importance of the power of a hypothesis test

• Know that sample size can be changed to

potentially elicit appropriate evidence in a

hypothesis test

• Interpret Type I and Type II errors, in

hypothesis testing and know their practical

meaning

• Calculate the risk of a Type II error

• Know the difference and advantages of using

critical regions or p-values as appropriate in

real life contexts in all tests in this subject

x

− ± z or t × standard errorStudents will be expected to know and recallthat:

• a Type I error is when the null hypothesis istrue but is rejected

• a Type II error is when the null hypothesis isfalse but is accepted

and that these should be interpreted in thegiven context

Students are expected to know and recall thatthe power of a test is given by

Power = 1 – P(Type II error)

DRAFT

3.16 Hypothesis testing for 1 and 2 samples

Know how to apply knowledge about carrying

out hypothesis testing to conduct tests for the:

• mean of a normal distribution with unknown

variance using the t distribution

• difference of two means for two independent

normal distributions with known variances

• difference of two means for two independent

normal distributions with unknown but equal

variances

• difference between two binomial proportions

• interpret results for these tests in context

Together with the content already mentioned inA1.8, candidates will be given and expected toselect and use the following:

• test statistic for a mean using t distribution:

X

− −μ

S n

tn− 1

• test statistic for difference of twoindependent normal means with knownvariances :