CAIE S2 2011 November — Question 2 5 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2011
SessionNovember
Marks5
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Mark schemeDownload PDF ↗
TopicApproximating Binomial to Normal Distribution
TypeOne-tailed hypothesis test
DifficultyStandard +0.3 This is a straightforward one-tailed hypothesis test using normal approximation to binomial with standard parameters (n=100, p=0.2). It requires routine application of continuity correction, z-score calculation, and comparison to critical value—all standard S2 techniques with no conceptual challenges or novel problem-solving required.
Spec2.04d Normal approximation to binomial2.05c Significance levels: one-tail and two-tail5.02c Linear coding: effects on mean and variance
2 An engineering test consists of 100 multiple-choice questions. Each question has 5 suggested answers, only one of which is correct. Ashok knows nothing about engineering, but he claims that his general knowledge enables him to get more questions correct than just by guessing. Ashok actually gets 27 answers correct. Use a suitable approximating distribution to test at the \(5 \%\) significance level whether his claim is justified.
Question 2:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(H_0: P(\text{correct}) = \frac{1}{5}\), \(H_1: P(\text{correct}) > \frac{1}{5}\), \(B(100, \frac{1}{5}) \approx N(20, 16)\)B1 Accept \(p\); Accept \(H_0: \mu = 20\), \(H_1: \mu > 20\)
\(\dfrac{26.5 - 20}{4} = 1.625\)M1 A1 A1 Allow wrong or no cc or denom \(= 16\); For \(\pm 1.625\)
comp \(z = 1.645\)M1 Valid comparison of \(z\) or areas \((0.0521 > 0.05)\)
Claim not justifiedA1ft [5] In context. No contradictions. Ft their \(z\) 
## Question 2:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $H_0: P(\text{correct}) = \frac{1}{5}$, $H_1: P(\text{correct}) > \frac{1}{5}$, $B(100, \frac{1}{5}) \approx N(20, 16)$ | B1 | Accept $p$; Accept $H_0: \mu = 20$, $H_1: \mu > 20$ |
| $\dfrac{26.5 - 20}{4} = 1.625$ | M1 A1 A1 | Allow wrong or no cc or denom $= 16$; For $\pm 1.625$ |
| comp $z = 1.645$ | M1 | Valid comparison of $z$ or areas $(0.0521 > 0.05)$ |
| Claim not justified | A1ft [5] | In context. No contradictions. Ft their $z$ |

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2 An engineering test consists of 100 multiple-choice questions. Each question has 5 suggested answers, only one of which is correct. Ashok knows nothing about engineering, but he claims that his general knowledge enables him to get more questions correct than just by guessing. Ashok actually gets 27 answers correct. Use a suitable approximating distribution to test at the $5 \%$ significance level whether his claim is justified.

\hfill \mbox{\textit{CAIE S2 2011 Q2 [5]}}
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