AQA 7387 SP 2017 v0 1

T DRAFT 7387 Specification For teaching from September 2017 onwards For A-level exams in 2019 onwards R AF DRAFT SPECIFICATION A-LEVEL STATISTICS D Version 0.1 11 August 2016 DRAFT SPECIFICATION T R AF D A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Contents Introduction 2.1 Subject content 2.2 Assessments 7 Subject content 3.1 Numerical measures, graphs and diagrams 3.2 Probability 3.3 Population and samples 3.4 Introduction to probability distributions 3.5 Binomial distribution 3.6 Normal distribution 3.7 Correlation and linear regression 3.8 Introduction to hypothesis testing 3.9 Contingency tables 3.10 One and two sample non-parametric tests 3.11 Bayes’ theorem 3.12 Probability distributions 3.13 Experimental design 3.14 Sampling, estimates and resampling 3.15 Hypothesis testing, significance testing, confidence intervals and power 3.16 Hypothesis testing for and samples 3.17 Paired tests 3.18 Exponential and Poisson distributions 3.19 Goodness of fit 3.20 Analysis of variance 3.21 Effect size 3.22 Statistical Enquiry Cycle (SEC) 10 11 11 12 12 13 14 15 16 16 17 17 18 18 D R AF DRAFT SPECIFICATION Specification at a glance 5 T 1.1 Why choose AQA for A-level Statistics 1.2 Support and resources to help you teach 1.3 Draft specification Scheme of assessment 4.1 Aims 4.2 Assessment objectives 4.3 Assessment weightings General administration 5.1 Entries and codes 5.2 Overlaps with other qualifications 19 20 21 21 22 22 23 23 25 25 25 26 27 27 27 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration R AF D Are you using the latest version of this specification? • • You will always find the most up-to-date version of this specification on our website at aqa.org.uk/7387 We will write to you if there are significant changes to the specification Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION 27 27 28 28 28 29 29 T 5.3 Awarding grades and reporting results 5.4 Re-sits and shelf life 5.5 Previous learning and prerequisites 5.6 Access to assessment: diversity and inclusion 5.7 Working with AQA for the first time 5.8 Private candidates 5.9 Use of calculators A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 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 T 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 R AF DRAFT SPECIFICATION It goes well with subjects including A-level Biology, Psychology, Geography, Business Studies and Economics 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 D 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 progress tests with engaging on-screen delivery and instant feedback training courses to help you deliver AQA Statistics qualifications subject expertise courses for all teachers, from newly qualified teachers who are just getting started to experienced teachers looking for fresh inspiration Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 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 T 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 R AF 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 updates at aqa.org.uk/from-2017 Alternatively, you can call or email our subject team direct E: maths@aqa.org.uk D T: 01483 477655 1.3 Draft specification 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 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION 1.2.3 Analyse your students' results with Enhanced Results Analysis (ERA) A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Specification at a glance This qualification is linear Linear means that students will sit all their exams at the end of the course Numerical measures, graphs and diagrams (page 10) Probability (page 11) 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 and 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) T • • • • • • • • • • • • • • • • • • • • • D R AF DRAFT SPECIFICATION 2.1 Subject content Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 2.2 Assessments Paper What's assessed Specification content 3.1‒3.10 Questions R AF • Questions requiring multiple choice, short, medium and extended answers including a Statistical Enquiry Cycle (SEC) question Paper What's assessed Specification content 3.11‒3.21, not precluding 3.1‒3.10 How it's assessed • Written exam: hours • 120 marks • 50% of A-level Questions D • Questions requiring multiple choice, short, medium and extended answers including a Statistical Enquiry Cycle (SEC) question Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION • Written exam: hours • 120 marks • 50% of A-level T How it's assessed A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 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 T In addition to this subject content, students should be able to recall, select and apply mathematical formulae See Appendix (page 31) and Appendix (page 33) for a list of the DfE prescribed formulae D R AF DRAFT SPECIFICATION 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 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 3.1 Numerical measures, graphs and diagrams Subject content Additional information • 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 construct statistical diagrams Students must learn and recall the following: • the angle in a pie chart is given by x × 360 total f requency class width f requency densit y = • the formula for calculating the arithmetic mean is ∑fx ∑f R AF − x= • range is highest value–smallest value • Interquartile range (IQR) = Q3 – Q1 where Q1 is the 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 ± 3σ Students will be given the following information Population variance = N ∑ x − μ Population standard deviation = Sample variance = n − ∑ x − − x D Sample standard deviation = 10 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration N n−1 ∑ x−μ ∑ x−− x 2 DRAFT SPECIFICATION T • in a histogram • to collect and represent data • to calculate summary statistics and probabilities • in relation to hypotheses and inference • AO2: Interpret statistical information and results in context and reason statistically to make predictions, construct arguments, make decisions and draw conclusions • AO3: Critically assess the reliability and validity of statistical methodologies and the conclusions drawn through the application of the statistical enquiry cycle 4.2.1 Assessment objective weightings for A-level Statistics Assessment objectives (AOs) Component weightings (approx %) +/-2% Overall weighting (approx %) +/-2% AO2 AO3 55 55 25 25 25 20 20 20 50 50 100 R AF Overall weighting of components 55 4.3 Assessment weightings The marks awarded on the papers will be scaled to meet the weighting of the components Students’ final marks will be calculated by adding together the scaled marks for each component Grade boundaries will be set using this total scaled mark The scaling and total scaled marks are shown in the table below Component Maximum raw mark Scaling factor Maximum scaled mark Paper 120 x1 120 Paper 120 x1 120 D Total scaled mark: 240 26 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION AO1 T Paper Paper A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 General administration You can find information about all aspects of administration, as well as all the forms you need, at aqa.org.uk/examsadmin 5.1 Entries and codes T Every specification is given a national discount (classification) code by the Department for Education (DfE), which indicates its subject area If a student takes two specifications with the same discount code, further and higher education providers are likely to take the view that they have only achieved one of the two qualifications Please check this before your students start their course R AF DRAFT SPECIFICATION You only need to make one entry for each qualification – this will cover all the question papers, non-exam assessment and certification Qualification title AQA entry code DfE discount code AQA Advanced Level GCE in Statistics 7387 TBC This specification complies with: • • • • Ofqual General conditions of recognition that apply to all regulated qualifications Ofqual GCE qualification level conditions that apply to all GCEs Ofqual GCE subject level conditions that apply to all GCEs in this subject all other relevant regulatory documents The Ofqual qualification accreditation number (QAN) is TBC 5.2 Overlaps with other qualifications There is overlapping content in the AS and A-level Statistics specifications This helps you teach the AS and A-level together D 5.3 Awarding grades and reporting results The A-level qualification will be graded on a six-point scale: A*, A, B, C, D and E Students who fail to reach the minimum standard for grade E will be recorded as U (unclassified) and will not receive a qualification certificate 5.4 Re-sits and shelf life Students can resit the qualification as many times as they wish, within the shelf life of the qualification Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 27 5.5 Previous learning and prerequisites AS and A-level Statistics specifications assume a basic level of numerical skills, as listed in Appendix (page 37), as studied in GCSE Mathematics 5.6 Access to assessment: diversity and inclusion T The subject criteria have been assessed to see if any of the skills or knowledge required present any possible difficulty to any students, whatever their ethnic background, religion, sex, age, disability or sexuality Tests of specific competences were only included if they were important to the subject R AF As members of the Joint Council for Qualifications (JCQ) we participate in the production of the JCQ document Access Arrangements and Reasonable Adjustments: General and Vocational qualifications We follow these guidelines when assessing the needs of individual students who may require an access arrangement or reasonable adjustment This document is published at jcq.org.uk Students with disabilities and special needs We're required by the Equality Act 2010 to make reasonable adjustments to remove or lessen any disadvantage that affects a disabled student We can make arrangements for disabled students and students with special needs to help them access the assessments, as long as the competences being tested aren't changed Access arrangements must be agreed before the assessment For example, a Braille paper would be a reasonable adjustment for a Braille reader To arrange access arrangements or reasonable adjustments, you can apply using the online service at aqa.org.uk/eaqa Special consideration We can give special consideration to students who have been disadvantaged at the time of the assessment through no fault of their own – for example a temporary illness, injury or serious problem such as family bereavement We can only this after the assessment D Your exams officer should apply online for special consideration at aqa.org.uk/eaqa For more information and advice visit aqa.org.uk/access or email accessarrangementsqueries@aqa.org.uk 5.7 Working with AQA for the first time If your school or college hasn't previously offered our specifications, you need to register as an AQA centre Find out how at aqa.org.uk/becomeacentre 28 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION General qualifications are designed to prepare students for a wide range of occupations and further study Therefore our qualifications must assess a wide range of competences A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 5.8 Private candidates This specification is available to private candidates A private candidate is someone who enters for exams through an AQA approved school or college but is not enrolled as a student there A private candidate may be self-taught, home schooled or have private tuition, either with a tutor or through a distance learning organisation They must be based in the UK 5.9 Use of calculators T • speak to the exams officer at the school or college where you intend to take your exams • visit our website at aqa.org.uk/privatecandidates • email privatecandidates@aqa.org.uk Students may use a calculator in the exam They must ensure that their calculator meets the requirements as set out in the JCQ Instructions for conducting examinations These instructions make it clear what the requirements are for calculators (what they must be) and what they are not (what they must not be) The instructions are regularly updated and can be found at jcq.org.uk D R AF DRAFT SPECIFICATION If you have any queries as a private candidate, you can: Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 29 DRAFT SPECIFICATION T R AF D 30 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Appendix Statistical formulae for A-level statistics that students are expected to learn and will not be given in the assessment Content reference Formula required A1.1 Calculating the angle for a sector in a pie chart: Frequency density for a histogram: f equency frequency density = class width A1.1 Calculation of arithmetic mean: R AF DRAFT SPECIFICATION A1.1 × 360 T x 100 A1.1 − x= ∑fx f Range = highest value – lowest value A1.1 Interquartile range (IQR) = upper quartile – lower quartile A1.1 Identification of an outlier: Lower outlier is < LQ – 1.5IQR Upper outlier is > UQ + 1.5IQR Outlier is also outside μ ± 3σ A1.2 Formulae for independent events: P(A∩B) = P(A)P(B) D P(A l B) = P(A) and P(B l A) = P(B) A1.3 A1.4 In order to carry out stratification, calculating the percentage or proportion of an amount: x 100 × amount Properties of discrete random variables: expectation (mean): E X = μ = ∑ xi pi 2 variance: Var X = σ = ∑ xi − μ pi 2 2 = ∑ xi pi − μ = E X − μ Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 31 Content reference Formula required A2.6 Other confidence intervals: 32 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION D R AF T several variations on estimate ± t or z value x standard error according to the particular confidence interval A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Appendix Statistical formulae for A-level statistics that students are expected to be familiar with and will be given in the assessment, either with the question or as a separate formulae sheet or booklet Content reference Formula required A1.1 Population variance = N ∑ x − μ ∑ x−μ T A1.1 x Sample variance = n − ∑ x − − Sample standard deviation = N n−1 ∑ x−− x R AF DRAFT SPECIFICATION Population standard deviation = A1.5 Binomial probability calculations: P X =x = n x Mean = np px − p n − x Variance = np(1- p) A1.7 Test statistic for a mean using normal distribution: − X −μ σ n N 0,1 Test statistic for a binomial proportion using normal distribution: p− p p 1− p n D A1.8 A2.1 A2.2 N 0,1 Formula for chi-squared test ∑ Oi− Ei Ei Bayes’ theorem for up to three events: P Aj B = P Aj n ∑i = P × P B Aj Ai × P B Ai The Poisson probability formula: x P X = x = e− λ λx ! and knowledge of the mean and variance both being λ Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 33 Content reference Formula required A2.2 The exponential cumulative probability formula: P X ≤ x = − e− λx 1 and knowledge of the mean and variance being λ and λ respectively A2.3 E XY = E X E Y 2 but E X + Y = E X + E Y not given A2.7 Test statistic for a mean using t distribution: − X −μ tn − R AF S n A2.7 Test statistic for difference of two independent normal means with known variances: − − X − Y − μx − μ y A2.7 σ 2x nx σ2 + ny y Test statistic for difference of two independent normal means with unknown but equal variance: − − X − Y − μx − μ y S 2p S 2p = A2.7 D A2.9 +n nx y tnx + n y − where nx − S 2x + n y − S 2y nx + n y − Test statistic for the difference in two binomial proportions: p1 p2 s error A2.8 N 0,1 where s error = where p = p1 × n1 + p2 × n2 n1 + n2 p× 1− p × n1 +n Paired t-test: − X −μ S n tn − Test for association and goodness of fit test: ∑ Oi − Ei Ei is approximately distributed as X 34 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION T Var aX ± bY = a Var X + b Var Y A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Content reference Formula required A2.10 Analysis of variance (one-way and two-way): one − factor model xi j = μ + + εi j, where εi j N 0, σ 2 T2 total sum of squares SS T = ∑i ∑ j xi j − n T2 T2 between groups sum of squares SS B = ∑i ni − n i T xi j = μ + + β j + εi j, where εi j N 0, σ 2 T2 total sum of squares SS T = ∑i ∑ j xi j − mn R2 T2 between rows sum of squares SS R = ∑i ni − mn R AF DRAFT SPECIFICATION two − factor model with m rows and n columns C2 A2.11 Cohen’s d formula: d= x−1 − x−2 s n1 − s21 + n2 − s22 n1 + n2 − where s = A2.12 Spearman’s correlation coefficient: 6∑ d A2.12 D rs = − n n2 −i1 Product moment correlation coefficient: r= A2.12 T2 between columns sum of squares SS c = ∑i mj − mn = S xy S xx × S yy ∑ xi yi − ∑ xi − ∑ xi n ∑ xi − − x yi − − y = ∑ xi − − x ∑ xi ∑ yi ∑ yi − − y n ∑ yi − ∑ yi n Coefficients for least squares regression line: least squares regression line of y on x is y = a + bx, where a=− y − b− x S the regression coefficient of y on x is b = S xy = xx ∑ xi − − x yi − − y − ∑ x −x i Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 35 DRAFT SPECIFICATION T R AF D 36 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Appendix The numerical skills, developed in GCSE (9-1) mathematics, required for A-level statistics Integers, fractions, decimals and percentages T • Identify and work with fractions in ratio problems • Interpret fractions and percentages as operators Structure and calculation R AF DRAFT SPECIFICATION • Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and or 0.375 or ), and recognise that some fractions can be written as recurring decimals • Order positive integers, decimals and fractions • Understand and use the symbols =, ≠, , ≤ and ≥ • Apply the four operations to integers, decimals and simple fractions (proper and improper), and mixed numbers • Understand and use place value (eg when working with very large or very small numbers, and when calculating with decimals) • Recognise, use and manipulate numbers in standard form • Recognise and use relationships between operations, including inverse operations (eg cancellation to simplify calculations and expressions; use conventional notation for priority of operations, including brackets, powers, roots and reciprocals) • Substitute numerical values into formulae and expressions, including scientific formulae • Understand and use standard mathematical formulae, and rearrange formulae to change the subject • Solve algebraic equations, including simultaneous equations • Work with coordinates on Cartesian grid Measures and accuracy D • Use standard units of mass, length, time, money and other measures (including standard compound measures) using decimal quantities where appropriate • Estimate answers and check calculations using approximation and estimation, including answers obtained using technology • Use compound units such as speed, rates of pay and unit pricing including working out a unit for a rate • Round numbers and measures to an appropriate degree of accuracy (eg to a specified number of decimal places or significant figures), and use inequality notation to specify simple error intervals due to truncation or rounding Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 37 Ratio, proportion and rates of change 38 Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION D R AF T • Express one quantity as a fraction of another, where the fraction is less than or greater than • Use ratio notation, including reduction to simplest form • Divide a given quantity into two parts in a given part, part or part, and whole ratio; express the division of a quantity into two parts as a ratio; and apply ratio to real contexts and problems (such as those involving probability) • Relate ratios to fractions and vice versa • Define percentage as ‘number of parts per hundred’; interpret percentages and percentage changes as a fraction or a decimal, and interpret these multiplicatively; express one quantity as a percentage of another; and compare two quantities using percentages A-level Statistics DRAFT 7387 A-level exams June 2019 onwards Version 0.1 11 August 2016 Appendix Specifications must encourage the application of techniques within the framework of the statistical enquiry cycle using real data taken from authentic contexts identifying factors that may be related to the problem under investigation defining a question or hypothesis (or hypotheses) to investigate deciding what data to collect, and how to collect and record it, giving reasons engaging in exploratory data analysis in order to investigate the situation developing a strategy for how to process and represent the data giving reasons justifying the proposed plan with regards ensuring a lack of bias T • • • • • • Specifications must enable students to recognise the constraints involved in sourcing data including: R AF DRAFT SPECIFICATION Specifications must require students to understand the importance of initial planning when designing a line of enquiry or investigation including: • when designing unbiased collection methods for primary sample data • when researching sources of secondary data, including from reference publications, the internet and the media • recognise the importance of declaring the data collection methodology, including appreciating the importance of acknowledging sources • appreciating the inherent bias that may be incorporated through the use of leading questions either by accident or through agenda driven design Students must understand a range of techniques in order to process, represent and discuss data including: • organising and processing data, including an understanding of how technology can be used • make inferences about the population using appropriately chosen diagrams and summary measures to represent data including an understanding of outputs generated by appropriate technology • appreciating how to avoid misrepresentation of data Students must appreciate the need to consider the context of the problem when interpreting results: analysing/interpreting diagrams and calculations/measures drawing together conclusions that relate to the questions and hypotheses addressed using appropriate tests to determine the statistical significance of the findings discussing the reliability of findings D • • • • Specifications must require students to show an understanding of the importance of the clear and concise communication of findings and key ideas, and awareness of target audience Students must be able to understand the importance of evaluating statistical work including: • • • • identifying weaknesses in approaches used to collect or display data recognising the limitations of findings by considering sample size and sampling technique suggesting improvements to statistical processes or presentation refining processes to elicit further clarification of the initial hypothesis Visit aqa.org.uk/7387 for the most up-to-date specification, resources, support and administration 39 Get help and support Visit our website for information, guidance, support and resources at aqa.org.uk/7387 You can talk directly to the Statistics subject team: E: maths@aqa.org.uk aqa.org.uk Copyright © 2015 AQA and its licensors All rights reserved AQA retains the copyright on all its publications, including the specifications However, schools and colleges registered with AQA are permitted to copy material from this specification for their own internal use AQA Education (AQA) is a registered charity (number 1073334) and a company limited by guarantee registered in England and Wales (company number 3644723) Our registered address is AQA, Devas Street, Manchester M15 6EX DRAFT SPECIFICATION D R AF T T: 01483 477655 [...]... Maximum scaled mark Paper 1 120 x1 12 0 Paper 2 12 0 x1 12 0 D Total scaled mark: 240 26 Visit aqa. org.uk /7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION AO1 T Paper 1 Paper 2 A-level Statistics DRAFT 7387 A-level exams June 2 019 onwards Version 0 .1 11 August 2 016 5 General administration You can find information about all aspects of administration,... A2.7 D A2.9 1 +n nx y tnx + n y − 2 where nx − 1 S 2x + n y − 1 S 2y nx + n y − 2 Test statistic for the difference in two binomial proportions: p1 p2 s error A2.8 N 0 ,1 where s error = where p = p1 × n1 + p2 × n2 n1 + n2 p× 1 p × 1 n1 1 +n 2 Paired t-test: − X −μ S n tn − 1 Test for association and goodness of fit test: ∑ Oi − Ei 2 Ei is approximately distributed as X 34 Visit aqa. org.uk /7387 for... mn R2 T2 between rows sum of squares SS R = ∑i ni − mn R AF DRAFT SPECIFICATION two − factor model with m rows and n columns C2 A2 .11 Cohen’s d formula: d= x 1 − x−2 s n1 − 1 s 21 + n2 − 1 s22 n1 + n2 − 2 where s = A2 .12 Spearman’s correlation coefficient: 6∑ d A2 .12 D 2 rs = 1 − n n2 −i1 Product moment correlation coefficient: r= A2 .12 T2 between columns sum of squares SS c = ∑i mj − mn = S xy S xx... DRAFT SPECIFICATION If you have any queries as a private candidate, you can: Visit aqa. org.uk /7387 for the most up-to-date specification, resources, support and administration 29 DRAFT SPECIFICATION T R AF D 30 Visit aqa. org.uk /7387 for the most up-to-date specification, resources, support and administration A-level Statistics DRAFT 7387 A-level exams June 2 019 onwards Version 0 .1 11 August 2 016 Appendix... DRAFT 7387 A-level exams June 2 019 onwards Version 0 .1 11 August 2 016 Appendix 2 Statistical formulae for A-level statistics that students are expected to be familiar with and will be given in the assessment, either with the question or as a separate formulae sheet or booklet Content reference Formula required A1 .1 Population variance = N ∑ x − μ 1 2 1 ∑ x−μ 2 T A1 .1 x Sample variance = n − 1 ∑ x − − 1. .. rank-sum test (this is also known as the Mann-Whitney test) 16 Visit aqa. org.uk /7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION Students may use either 'independent' or 'associated' in their hypotheses A-level Statistics DRAFT 7387 A-level exams June 2 019 onwards Version 0 .1 11 August 2 016 3 .11 Bayes’ theorem Subject content Additional information... S 2x + n y − 1 S 2y nx + n y − 2 • test statistic for the difference in two binomial proportions: p1 p2 s error where s error = p1 × n1 + p2 × n2 n1 + n2 D and where p = p× 1 p × 20 Visit aqa. org.uk /7387 for the most up-to-date specification, resources, support and administration 1 n1 1 +n 2 DRAFT SPECIFICATION − X −μ T • mean of a normal distribution with unknown variance using the t distribution... Sample standard deviation = N 2 1 n 1 ∑ x−− x 2 R AF DRAFT SPECIFICATION Population standard deviation = A1.5 Binomial probability calculations: P X =x = n x Mean = np px 1 − p n − x Variance = np (1- p) A1.7 Test statistic for a mean using normal distribution: − X −μ σ n N 0 ,1 Test statistic for a binomial proportion using normal distribution: p− p p 1 p n D A1.8 A2 .1 A2.2 N 0 ,1 Formula for chi-squared... use the central limit theorem when the underlying population is not normally distributed 18 Visit aqa. org.uk /7387 for the most up-to-date specification, resources, support and administration DRAFT SPECIFICATION Subject content A-level Statistics DRAFT 7387 A-level exams June 2 019 onwards Version 0 .1 11 August 2 016 Subject content Additional information • Use confidence intervals for the mean using z... 2 016 Appendix 1 Statistical formulae for A-level statistics that students are expected to learn and will not be given in the assessment Content reference Formula required A1 .1 Calculating the angle for a sector in a pie chart: Frequency density for a histogram: f equency frequency density = class width A1 .1 Calculation of arithmetic mean: R AF DRAFT SPECIFICATION A1 .1 × 360 T x 10 0 A1 .1 − x= ∑fx f Range