A-LEVEL Statistics. SS1B Statistics 1B Final Mark Scheme June Version/Stage: v1.0

Transcription

1 A-LEVEL Statistics SS1B Statistics 1B Final Mark Scheme 6380 June 017 Version/Stage: v1.0

2 Mark schemes are prepared by the Lead Assessment Writer and considered, together with the relevant questions, by a panel of subject teachers. This mark scheme includes any amendments made at the standardisation events which all associates participate in and is the scheme which was used by them in this examination. The standardisation process ensures that the mark scheme covers the students responses to questions and that every associate understands and applies it in the same crect way. As preparation f standardisation each associate analyses a number of students scripts. Alternative answers not already covered by the mark scheme are discussed and legislated f. If, after the standardisation process, associates encounter unusual answers which have not been raised they are required to refer these to the Lead Assessment Writer. It must be stressed that a mark scheme is a wking document, in many cases further developed and expanded on the basis of students reactions to a particular paper. Assumptions about future mark schemes on the basis of one year s document should be avoided; whilst the guiding principles of assessment remain constant, details will change, depending on the content of a particular examination paper. Further copies of this mark scheme are available from aqa.g.uk Copyright 017 AQA and its licenss. All rights reserved. AQA retains the copyright on all its publications. However, registered schools/colleges f AQA are permitted to copy material from this booklet f their own internal use, with the following imptant exception: AQA cannot give permission to schools/colleges to photocopy any material that is acknowledged to a third party even f internal use within the centre.

3 Key to mark scheme abbreviations M mark is f method m dm mark is dependent on one me M marks and is f method A mark is dependent on M m marks and is f accuracy B mark is independent of M m marks and is f method and accuracy E mark is f explanation ft F follow through from previous increct result CAO crect answer only CSO crect solution only AWFW anything which falls within AWRT anything which rounds to ACF any crect fm AG answer given SC special case OE equivalent A,1 1 ( 0) accuracy marks x EE deduct x marks f each err NMS no method shown PI possibly implied SCA substantially crect approach c candidate sf significant figure(s) dp decimal place(s) No Method Shown Where the question specifically requires a particular method to be used, we must usually see evidence of use of this method f any marks to be awarded. Where the answer can be reasonably obtained without showing wking and it is very unlikely that the crect answer can be obtained by using an increct method, we must award full marks. However, the obvious penalty to candidates showing no wking is that increct answers, however close, earn no marks. Where a question asks the candidate to state write down a result, no method need be shown f full marks. Where the permitted calculat has functions which reasonably allow the solution of the question directly, the crect answer without wking earns full marks, unless it is given to less than the degree of accuracy accepted in the mark scheme, when it gains no marks. Otherwise we require evidence of a crect method f any marks to be awarded. 17/07/017 11:3 3 of 1

4 General f SS1B GN1 GN GN3 GN4 GN5 GN6 There is no allowance f misreads (MR) miscopies (MC) unless specifically stated in a question. In general, a crect answer (to accuracy required) without wking sces full marks but an increct answer ( an answer not to required accuracy) sces no marks. In general, a crect answer (to accuracy required) without units sces full marks. When applying AWFW, a slightly inaccurate numerical answer that is subsequently rounded to fall within the accepted range cannot be awarded full marks. Where percentage equivalent answers are permitted in a question, then penalise by one accuracy mark at the first crect answer but only if no indication of percentage (eg %) is shown. In questions involving probabilities, do not award accuracy marks f answers given in the fm of a ratio odds such as 13/47 given as 13:47 13:34. GN7 Accept decimal answers, providing that they have at least two leading zeros, in the fm c 10 -n (eg as ). GN8 Where a candidate's response to a part of a question is simply to label the part (eg (d)(i)) with nothing else (ie no attempt at a solution), then this is still treated as a response and marked as 0 rather than NR. Also, deleted wk, if not replaced, should be marked and not treated as NR. 17/07/017 11:3 4 of 1

5 1 (a) Median Names seen crectly somewhere in and (a) Interquartile Range Semi-Interquartile Range (i) Median (Q, m) = 31 CAO IQR = 34 SIQR = 17 B CAO; either 4 SC 1 If B0 in, then award f use of 47 (Q 3 ) 13 (Q 1 ); eg 4 13 = 9 Do not accept Q, m, IQR, SIQR, etc Mean = 33 CAO ( x = 495) Sd(n) = 0.4 to 0.5 Sd(n 1) = 1.1 to 1. B AWFW ( ) ( x = 617) AWFW (1.1888) Sd(n) Sd(n 1) = 0 to () 1 Value of variance stated as B0 Value of standard deviation stated as B0 490 to If, and only if, B0 B0, then award f seen attempt at ( ) 3 AWFW Total 7 17/07/017 11:3 5 of 1

6 (a) b (gradient/slope) = to B AWFW ( ) b (gradient/slope) = 0.5 to 0.6 () AWFW a (intercept) = 50.9 to 51.0 a (intercept) = 46 to 53 y = (46 to 53) (0.5 to 0.6)x B () AWFW ( ) AWFW OR Attempt at x Attempt at S xx & S xy x y & xy Attempt at substitution into crect cresponding fmula f b () (m1) & (all 4 attempted) ( y = ) & 19.5 (both attempted) (S yy = 19.4) b = to a = 50.9 to 51.0 (A1 A1) AWFW ( x = 57 & y = 18.) y = (46 to 53) (0.5 to 0.6)x 1 Values of a and b interchanged not identified but equation y = ax + b stated max of 5 marks Values of a and b interchanged not identified and equation y = a + bx stated 0 marks (i) y (60.0) = 16.3 to 16.6 AWFW ( ) 1 Women/sample selected could be: 5 Under 45 Over 65 Not between 45 and 65 OE; must reference age/years No previous browsing/it experience No internet/it access Accept "less experience" OE Accept "limited access" Total 8 17/07/017 11:3 6 of 1

7 3 Accept the equivalent percentage answers with %-sign (see GN5) (a)(i) Standardising 9 with 8.5 and 1.5; P(W < 9) = P Z < 1. 5 allow (8.5 9) (iii) (iv) = P(Z < 0.6) = 0.75 to 0.76 A1 AWFW (0.7575) () P(W > 8) = P(Z > 0.) = P(Z < 0.) CAO; igne sign P(W 8.5) = 1 one unity 100% P(8 < W < 10) = P( 0. < Z < 1.4) = AWRT (0.5796) () (1) CAO; accept nothing else but igne zeros after decimal point (eg 1.00) Igne additional wds providing that they are not contradicty (eg certain so = 1) = (1 ) = to B AWFW ( ) () 7 µ = 15 CAO; (by symmetry).5% z = 1.96 AWRT; igne sign (0 15)/σ = 1.96 (10 15)/σ = σ = 5 OE; crect equation σ =.55 A1 AWRT (.5510) OR.5% z = 1.96 () AWRT; igne sign (0 µ)/σ = 1.96 µ σ = 0 (10 µ)/σ = 1.96 µ 1.96σ = 10 () OE; two crect equations σ =.55 (A1) AWRT (.5510) µ = 15.0 () AWRT ( to 15.00) 4 Total 11 17/07/017 11:3 7 of 1

8 4 Accept the equivalent percentage answers with %-sign (see GN5) (a) (i) P(A B) = = /0 CAO; accept 65/100 (1) P(A B) = = /100 CAO (1) (iii) P(A B) = = /5 CAO; accept 56/100 8/50 (1) 3 (i) P(C D E ) = (iii) (iv) = 0.76 to A1 AWFW ( ) () P(C D E) = = to AWFW ( ) (1) P(1 late) = = = = P( late) = 1 P(0 1 late) = 1 ((i) + (iii)) Three combinations ( crect) = 0.19 to 0. A1 AWFW (0.190) () = 1 ( ) = 0.0 to 0.01 A1 AWFW (0.00) OR P( late) = P( 3 late) = = = = = () Requires addition of ( of 1 st 3 terms) and (4 th term) = 0.0 to 0.01 (A1) AWFW (0.00) () 7 Total 10 17/07/017 11:3 8 of 1

9 5 (a)(i) r = 0.54 to 0.55 B3 AWFW ( ) r = 0.5 to 0.6 (B) AWFW r = 0. to 0.3 () AWFW Attempt at x x y Attempt at S xx S yy & S xy y & xy () & (all 5 attempted) & (all 3 attempted) Attempt at substitution into crect cresponding fmula f r (m1) r = 0.54 to 0.55 (A1) AWFW 3 Weak/little negative (linear) crelation Bdep1 Dependent on 0.3 r 0. 1 Statements must include the wds weak little and negative together with crelation association relationship ; igne additional comments unless clearly contradicty Use of the following additional terms (in conjunction with weak little); fairly quite very Bdep1 3 Use of any of the following terms (even in conjunction with weak little): low small slight po some mild reasonably relatively pretty Bdep0 between (actual) fuel consumption and mileage mark-up of new CARS 1 As fuel consumption of cars increases so does mileage mark-up (OE) Bdep0 As fuel consumption/x increases so does mileage mark-up/y (OE) Bdep0 B0 (i) r = Context; providing 1 < r < 1 = to A1 AWFW ( ) F petrol-engine cars A1 to F1: Clear consistent distinction moderate some positive crelation Bdep1 Dependent on 0.6 r 0.7 between (actual) fuel consumption and mileage mark-up of new cars Context; (providing 1 < r < 1) F diesel-engine cars A to F: () Only if not sced above f petrol-engine cars Strong negative crelation between (actual) fuel consumption and mileage mark-up of new cars () Only if not sced above f petrol-engine cars 1 Only accept moderate some and strong with no additional terms Only accept positive (linear) crelation and negative (linear) crelation 4 Total 11 17/07/017 11:3 9 of 1

10 6 Accept 3 dp rounding of probabilities from tables Accept the equivalent percentage answers with %-sign (see GN5) (a) R: No S: Yes T: No OE; all three stated Grouped statements are not permitted below R: p is not constant / events not independent OE; B0 f 'without replacement' S: n = 10 p = 5/0 1/4 0.5 CAO CAO (i) (iii) T: n is not fixed/known/stated OE P(B = 3) = ( ) ( ) = P(B 5) = Crect expression Can be implied by a crect answer Igne additional expressions = 0.55 to 0.56 A1 AWFW (0.5561) () P(B 3) = AWRT (0.4711) (1) = to A1 AWFW (0.7367) Note (iv) = to () () 1 F calculation of individual terms no method: award B f to (AWFW); f to (AWFW) P(5 < B 1) = P(6 B 1) = MINUS ( ) (p 1 ) ( ) (p ) = 0.75 to A1 AWFW (0.7505) (3) 1 F calculation of individual terms no method: award B3 f 0.75 to (AWFW); B f to (AWFW); B f to (AWFW); B f to (AWFW) (1 p ) (1 p 1 ) A1 8 Total 13 17/07/017 11:3 10 of 1

11 7(a) x = = 59.5 CAO s = = 0.61 s = σ = = 0.56 σ = AWRT ( & ) Igne any notation AWRT (0.556 & ) CI f µ is 98% (0.98) z =.3 to.33 AWFW (.363).3to.33.05to ±.40 to to.1 Hence 59.5 ± (0.16 to 0.18) (( ) AWRT ) M,1 ( 1 ee) Igne any notation M0 if CI is not of the fm: ( z t) ( ) C ± D ; allow any combination in last term CAO/AWFW (0.167 to 0.175) Adep1 Dependent on award of M Note (59.3 to 59.34, to 59.68) 1 If award of M0 0r is followed by a numerically crect CI possibly solutions 6 AWFW; dp y = ( ) = 58.0 CAO; accept 58 99% (0.99) z =.57 to.58 99% (0.99) t =.7 to.73 AWFW (.5758) AWFW (.74) (.3 to.73) s w = Y 36 ( ) ( ) z t s = 3.7 = Y A1 36 OE; crect expression f CI width but allow missing Requires (3.7 OE) and (.57 to.58) (.7 to.73) and ( 36 6) 1 3 s Y = 4.31 ( ) A1 CAO 5 (.3 to.73) s Y ( 56.15, 59.85) y ± 36 = (OE) Crect z/t and crect subtraction A (.3 to.73) s Y = (OE) 36 Crect z/t A1 y + (.3 to.73) s Y = (OE) M0 36 Parts (a) & Total 11 17/07/017 11:3 11 of 1

12 7 Continued Parts (a) & Total 11 (c) Comparison of (sample) means Dubler weight mean ( x ) > Tiger weight mean ( y ) Bdep1 Dep on 58 and 59.5 and context is required Reference to sample is not required Comparison of CIs CIs overlap Bdep1 OE; dep on crect CI in (a) Conclusion Population means (may be) equal similar µ = µ X Y Bdep1 Dependent on both Bdep1 and Bdep1 Reference to population is required but context is not required Comparison of (sample) variability Dubler weight variability ( X X ) Tiger weight variability ( sy s Y) s s < 1 Dubler mean Tiger mean x > y BF0 Dubler variability Tiger variability sx sy SC s X Y Bdep1 1 If, and only if 0/4, then f either of: Dubler (bars) are heavier/weigh me than Tiger (bars) Dubler (bars) are less variable than Tiger (bars) s BF Must be a crect comparison using crect values from (a) and and context is required Reference to sample is not required 17/07/017 11:3 1 of 1