Pearson Progression Step Q Scheme Marks AOs and Progress descriptor 6a Let represent the number of bowls with minor defects 5th X (seen or implied). Find critical values and critical 0.2) may be implied XB(25, 3.4 M1 regions for a binomial P(X l) = 0.0274 ⩽ M1dep 1.1b distribution. P(X = 0) = 0.0038 1.1b A1 P(X 8) = 0.9532 P(X 9) = 0.0468  ⩽ ⩾ 1.1b M1 P(X 9) = 0.9827 P(X 10) = 0.0173  ⩽ ⩾ Critical region is = 0 10 X X ⩾ 1.1b A2 1.1b (6) 6b Significance level = 0.0038 + 0.0173 B1 1.2 6th Calculate actual = 0.0211 or 2.11% significance levels for a binomial distribution test. (1) 6c H0: = 0.2; H1: < 0.2 B1 2.5 5th p p Carry out 1-tail tests for the Let represent number of with minor defects M1 3.4 Y binomial (Under H0) 0.2) (may be implied) distribution. Y~B(20, Either B1 1.1b P(Y 2) = 0.2061 ⩽ 1.1b 0.2061 > 0.1 (or 10%) M1 Insufficient evidence at the 10% to suggest that the A1 3.2b proportion of defective bowls has decreased. Or P(Y 2) = 0.2061 B1 1.1b ⩽ P(Y 1) = 0.0692 so critical region is 1 Y M1 1.1b ⩽ ⩽ Insufficient evidence at the 10% level to suggest that the A1 3.2a proportion of defective bowls has decreased. 0.2061 > 0.10 or 0.7939 < 0.9 (5) (12
Q Scheme Marks AOs Pearson Progression Step and Progress descriptor 6a Let X represent the number of bowls with minor defects (seen or implied). XB(25, 0.2) may be implied P(X ⩽ l) = 0.0274 P(X = 0) = 0.0038 P(X ⩽ 8) = 0.9532  P(X ⩾ 9) = 0.0468 P(X ⩽ 9) = 0.9827  P(X ⩾ 10) = 0.0173 Critical region is X = 0 X ⩾ 10 M1 M1dep A1 M1 A2 3.4 1.1b 1.1b 1.1b 1.1b 1.1b 5th Find critical values and critical regions for a binomial distribution. (6) 6b Significance level = 0.0038 + 0.0173 = 0.0211 or 2.11% B1 1.2 6th Calculate actual significance levels for a binomial distribution test. (1) 6c H0: p = 0.2; H1: p < 0.2 B1 2.5 5th Carry out 1-tail tests for the binomial distribution. Let Y represent number of with minor defects (Under H0) Y~B(20, 0.2) (may be implied) M1 3.4 Either P(Y ⩽ 2) = 0.2061 0.2061 > 0.1 (or 10%) Insufficient evidence at the 10% to suggest that the proportion of defective bowls has decreased. Or P(Y ⩽ 2) = 0.2061 P(Y ⩽ 1) = 0.0692 so critical region is Y ⩽ 1 Insufficient evidence at the 10% level to suggest that the proportion of defective bowls has decreased. 0.2061 > 0.10 or 0.7939 < 0.9 B1 M1 A1 B1 M1 A1 1.1b 1.1b 3.2b 1.1b 1.1b 3.2a (5) (12
as_maths_statistics_unit_5_ms.docx