Pearson Progression Step Q Scheme Marks AOs and Progress descriptor 1a Two from: 5th B2 1.2 Understand the Each bolt is either faulty or not faulty. binomial 1.2 The probability of a bolt being faulty (or not) may be distribution (and assumed constant. its notation) and its use as a model. Whether one bolt is faulty (or not) may be assumed to be independent (or does not affect the probability of) whether another bolt is faulty (or not). There is a fixed number (50) of bolts. A random sample. (2) 1b Let represent the number of faulty 5th X Find critical 0.25) M1 3.4 X~B(50, values and critical P(X 6) = 0.0194 M1dep 1.1b regions for a ⩽ P(X 7) = 0.0453 ⩽ binomial P(X 19) = 0.0287 ⩾ distribution. P(X 20) = 0.0139 ⩾ Critical Region is 6 20 A2 1.1b X X ⩽ ⩾ 1.1b (4) (6 marks) Notes 1a Each comment must be in context for its mark. Pearson Progression Step Q Scheme Marks AOs and Progress descriptor 2a The set of values of the test statistic for which the null B2 1.2 5th hypothesis is rejected in a hypothesis test. 1.2 Understand the language of hypothesis testing.
Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 1a Two from: Each bolt is either faulty or not faulty. The probability of a bolt being faulty (or not) may be assumed constant. Whether one bolt is faulty (or not) may be assumed to be independent (or does not affect the probability of) whether another bolt is faulty (or not). There is a fixed number (50) of bolts. A random sample. B2 1.2 1.2 5th Understand the binomial distribution (and its notation) and its use as a model. (2) 1b Let X represent the number of faulty X~B(50, 0.25) P(X ⩽ 6) = 0.0194 P(X ⩽ 7) = 0.0453 P(X ⩾ 19) = 0.0287 P(X ⩾ 20) = 0.0139 M1 M1dep 3.4 1.1b 5th Find critical values and critical regions for a binomial distribution. Critical Region is X ⩽ 6 X ⩾ 20 A2 1.1b 1.1b (4) (6 marks) Notes 1a Each comment must be in context for its mark. Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 2a The set of values of the test statistic for which the null hypothesis is rejected in a hypothesis test. B2 1.2 1.2 5th Understand the language of hypothesis testing.
as_maths_statistics_unit_5_ms.docx