Edexcel S2 — Question 2 6 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Marks6
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TopicHypothesis test of binomial distributions
TypeOne-tailed hypothesis test (lower tail, H₁: p < p₀)
DifficultyStandard +0.3 This is a straightforward one-tailed binomial hypothesis test with clearly defined parameters. Students must state hypotheses (H₀: p=0.12, H₁: p<0.12), calculate P(X≤1) under H₀ using B(25,0.12), and compare to 1% significance level. While it requires correct setup and binomial probability calculation, it's a standard S2 procedure with no conceptual surprises, making it slightly easier than average.
Spec2.05b Hypothesis test for binomial proportion
A certain type of lettuce seed has a 12\% failure rate for germination. In a new sample of 25 genetically modified seeds, only 1 did not germinate. Clearly stating your hypotheses, test, at the 1\% significance level, whether the GM seeds are better. [6 marks]
AnswerMarks Guidance
\(X \sim B(25, p)\)B1 B1
\(H_0: p = 0.12\) \(H_1: p < 0.12\)
Under \(H_0\), \(P(X = 0 \text{ or } 1) = 0.88^{25} + 25 \times 0.88^{24} \times 0.12 = 0.181 > 1\%\)M1 M1 A1
Therefore, no significant evidence in favour of \(H_1\) at the 1% levelA1 6 marks total 
$X \sim B(25, p)$ | B1 B1 |

$H_0: p = 0.12$ $H_1: p < 0.12$ | |

Under $H_0$, $P(X = 0 \text{ or } 1) = 0.88^{25} + 25 \times 0.88^{24} \times 0.12 = 0.181 > 1\%$ | M1 M1 A1 |

Therefore, no significant evidence in favour of $H_1$ at the 1% level | A1 | 6 marks total
A certain type of lettuce seed has a 12\% failure rate for germination. In a new sample of 25 genetically modified seeds, only 1 did not germinate.

Clearly stating your hypotheses, test, at the 1\% significance level, whether the GM seeds are better. [6 marks]

\hfill \mbox{\textit{Edexcel S2  Q2 [6]}}
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