Pearson Progression Step Q Scheme Marks AOs and Progress descriptor 5th H0: = 0.2 p 5a B1 2.5 Carry out 1-tail H1: > 0.2 p tests for the binomial Let represent the number of times the taxi is late. X M1 3.3 distribution. 0.2) seen or implied. X~B(5, Either P(X 3) = 1 P(X 2) = 1 0.9421 – – ⩾ ⩽ 1.1b M1 = 0.0579 A1 1.1b 0.0579 > 0.05 B1 1.1b There is insufficient evidence at the 5% significance level that B1 3.2a there is an increase in the number of times the taxi/driver is late. Or P(X 3) = 1 P(X 2) = 0.0579 – ⩾ ⩽ M1 1.1b P(X 4) = 1 P(X 3) = 0.0067 – ⩾ ⩽ So critical region is 4 X ⩾ A1 1.1b 3 < 4 or 3 is not in the critical region B1 1.1b So there is insufficient evidence at the 5% significance level that there is an increase in the number of times the taxi/driver is B1 3.2a late. (6) 5th 5b Two sensible reasons. For example, B2 2.2b Understand the Different time of the day travels to work. binomial 2.2b More traffic on different days (e.g. Monday morning, distribution (and Friday afternoon). its notation) and its use as a model. Weather conditions. Road (2) (8 marks) Notes Conclusion must be non-assertive.
Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 5a H0: p = 0.2 H1: p > 0.2 B1 2.5 5th Carry out 1-tail tests for the binomial distribution. Let X represent the number of times the taxi is late. X~B(5, 0.2) seen or implied. M1 3.3 Either P(X ⩾ 3) = 1 – P(X ⩽ 2) = 1 – 0.9421 = 0.0579 0.0579 > 0.05 There is insufficient evidence at the 5% significance level that there is an increase in the number of times the taxi/driver is late. Or P(X ⩾ 3) = 1 – P(X ⩽ 2) = 0.0579 P(X ⩾ 4) = 1 – P(X ⩽ 3) = 0.0067 So critical region is X ⩾ 4 3 < 4 or 3 is not in the critical region So there is insufficient evidence at the 5% significance level that there is an increase in the number of times the taxi/driver is late. M1 A1 B1 B1 M1 A1 B1 B1 1.1b 1.1b 1.1b 3.2a 1.1b 1.1b 1.1b 3.2a (6) 5b Two sensible reasons. For example, Different time of the day travels to work. More traffic on different days (e.g. Monday morning, Friday afternoon). Weather conditions. Road B2 2.2b 2.2b 5th Understand the binomial distribution (and its notation) and its use as a model. (2) (8 marks) Notes Conclusion must be non-assertive.