Version abc. General Certificate of Education. Mathematics MS2B Statistics 2. Mark Scheme examination - January series

Transcription

1 Version. 7 abc General Cerificae of Educaion Mahemaics 636 MSB Saisics Mark Scheme 7 examinaion - January series

2 MSB - AQA GCE Mark Scheme 7 January series Mark schemes are prepared by he Principal Examiner and considered, ogeher wih he relevan quesions, by a panel of subjec eachers. This mark scheme includes any amendmens made a he sandardisaion meeing aended by all examiners and is he scheme which was used by hem in his examinaion. The sandardisaion meeing ensures ha he mark scheme covers he candidaes responses o quesions and ha every examiner undersands and applies i in he same correc way. As preparaion for he sandardisaion meeing each examiner analyses a number of candidaes scrips: alernaive answers no already covered by he mark scheme are discussed a he meeing and legislaed for. If, afer his meeing, examiners encouner unusual answers which have no been discussed a he meeing hey are required o refer hese o he Principal Examiner. I mus be sressed ha a mark scheme is a working documen, in many cases furher developed and expanded on he basis of candidaes reacions o a paricular paper. Assumpions abou fuure mark schemes on he basis of one year s documen should be avoided; whils he guiding principles of assessmen remain consan, deails will change, depending on he conen of a paricular examinaion paper. Furher copies of his Mark Scheme are available o download from he AQA Websie: Copyrigh 7 AQA and is licensors. All righs reserved. COPYRIGHT AQA reains he copyrigh on all is publicaions. However, regisered cenres for AQA are permied o copy maerial from his bookle for heir own inernal use, wih he following imporan excepion: AQA canno give permission o cenres o phoocopy any maerial ha is acknowledged o a hird pary even for inernal use wihin he cenre. Se and published by he Assessmen and Qualificaions Alliance. The Assessmen and Qualificaions Alliance (AQA) is a company limied by guaranee regisered in England and Wales (company number ) and a regisered chariy (regisered chariy number 73334). Regisered address: AQA, Devas Sree, Mancheser M5 6EX Dr Michael Cresswell Direcor General

3 MSB - AQA GCE Mark Scheme 7 January series Key o mark scheme and abbreviaions used in marking M m or dm A B E mark is for mehod mark is dependen on one or more M marks and is for mehod mark is dependen on M or m marks and is for accuracy mark is independen of M or m marks and is for mehod and accuracy mark is for explanaion or f or F follow hrough from previous incorrec resul MC mis-copy CAO correc answer only MR mis-read CSO correc soluion only RA required accuracy AWFW anyhing which falls wihin FW furher work AWRT anyhing which rounds o ISW ignore subsequen work ACF any correc form FIW from incorrec work AG answer given BOD given benefi of doub SC special case WR work replaced by candidae OE or equivalen FB formulae book A, or (or ) accuracy marks NOS no on scheme x EE deduc x marks for each error G graph NMS no mehod shown C candidae PI possibly implied Sf significan figure(s) SCA subsanially correc approach Dp decimal place(s) No Mehod Shown Where he quesion specifically requires a paricular mehod o be used, we mus usually see evidence of use of his mehod for any marks o be awarded. However, here are siuaions in some unis where par marks would be appropriae, paricularly when similar echniques are involved. Your Principal Examiner will aler you o hese and deails will be provided on he mark scheme. Where he answer can be reasonably obained wihou showing working and i is very unlikely ha he correc answer can be obained by using an incorrec mehod, we mus award full marks. However, he obvious penaly o candidaes showing no working is ha incorrec answers, however close, earn no marks. Where a quesion asks he candidae o sae or wrie down a resul, no mehod need be shown for full marks. Where he permied calculaor has funcions which reasonably allow he soluion of he quesion direcly, he correc answer wihou working earns full marks, unless i is given o less han he degree of accuracy acceped in he mark scheme, when i gains no marks. Oherwise we require evidence of a correc mehod for any marks o be awarded. Jan 7 3

4 MSB - AQA GCE Mark Scheme 7 January series MSB x = s = 3.4 BB 4.53 σ =.5 s = ( ) cri =.365 B σ = ( ) 95% CI for µ s = x ± cri n 4.84 = 39.5 ± = 39.5 ± 4.5 M = ( 35.5,43.5) A 5 Toal e ( 3.5) 4 (a)(i) P ( A = 4) = =.89 MA 4! ± (ii) P( B 6) =.76 B (iii) T = A+ B Po ( 8.5) ( T ) = ( T < ) M Use of Po ( 8.5 ) = P( T 9) M T 9aemped P fewer han P =.653 A 3 CAO (b) X B( 5,.653) B X B5, ( heir p) 5 P 4 = ( X ) ( ) ( ) + (.653) 5 M = =.434 A 3 On heir p from (a)(iii) (c)(i) x = 9. s = 9.9 (ii) Mean and variance have similar values which suggess ha Poisson disribuion may be appropriae B B B B σ = 8.36 Toal 3 4

5 MSB - AQA GCE Mark Scheme 7 January series MSB (con) 3 x = 83.5 B s = = ( 54 < s 55) ( ) s = B (.4 s.45) H : µ = 85.9 H: 85.9 µ B (.44 ) Under H, X N 85.9, z cri =±.96 B z =.96 + ail es used ( heir x ) 85.9 z = = M ( heir s) / A AWFW.94 o.9 accep H, rejec he claim A On heir z 4(a) Insufficien evidence o sugges ha he mean has changed from 85.9 a he 5% level of significance. E 8 Toal 8 p = k = ( ) k =.38 B E = P = = 4.35 B (b)(i) ( X) x ( X x) all x (ii) Var ( ) P( ) 87 M ( X ) all x X = x X = x µ E aemped = M x P ( X = x ) µ =.675 A (AWFW.6.7) (c)(i) ( Y) ( X) E = 5E + = = 3.75 M Their (b)(i) 5 + (ii) Var( Y) = 5Var ( X) = Sandard deviaion = 5.4 M m A 3 Toal 9 Their (b)(ii) 5 ( ) 5

6 MSB - AQA GCE Mark Scheme 7 January series MSB (con) 5(a) H : µ = 3 H: µ > 3 B x = 33.5 and 4.5 Under H s = ( s = 8.6) BB σ =4.3 ( σ = 6.5) ( 4.5 ) X N 3, = = cri =.8 B do no rejec H Insufficien evidence a he % level of significance ha Jasmine s eacher is underesimaing he ime ha i akes o complee he homework assignmens. E 7 (b) Times are Normally disribued B Toal MA (.6.6) 4.3/ 9 6(a) B B B 3 for curve for line for axes 7 7 P T = = MA OE 8 8 (b) ( ) 6

7 MSB - AQA GCE Mark Scheme 7 January series MSB (con) 6(c)(i) For ( 5d ) + = MA F () = 8 5 F() = F() = ( 7) 3 + A 5 AG Alernaive: + ( ) 6 5d B 5 6 c (M) = + + (A) F () = 8 (B) c = 3.5 (M) F() ( 7) 3 (A) F F 5 d 6 M Use of: () = () + ( + ) (ii) ( 7).5 3 m + m = M m + m 3 = A 9 m = ± = 5± 48 = 5± 4 3 ( m > ) m = 4 3 5=.93 A 4 (.98) m Toal 4 (or any valid mehod) 7

8 MSB - AQA GCE Mark Scheme 7 January series MSB (con) 7(a) H : No associaion beween he performances a KS3 and GCE B O i E i Oi Ei X X = M M M M A E i O - E i ( - ) i O E E i i i AWFW ν = 3 = 6 χ 9% =.645 BB on heir ν Do no rejec H No evidence o sugges an associaion beween KS3 resuls and GCE grades a % level of significance. E 9 (b) More of he sudens achieving level 7 a KS3 gain grade A s a GCE han expeced. E Toal 8

9 MSB - AQA GCE Mark Scheme 7 January series MSB (con) 8(a) 4 x 5 f ( x) = 9 M A oherwise (b) B horizonal line from 4 o 5 B for drawn a 9 (c) P( X> ) = 3 9 = 3 M A ( ) F ( ) F5 = 3 = 3 (d) Mean = Variance = 8 B = 6.75 B Toal 8 TOTAL 75 9