Question 1 - A-Level Maths

CAIE S2 2010 November — Question 1 3 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2010
Session	November
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Confidence intervals
Type	Calculate CI for proportion
Difficulty	Easy -1.2 This is a straightforward application of the standard confidence interval formula for a proportion with a large sample size. It requires only direct substitution into a formula (p̂ ± z*√(p̂(1-p̂)/n)) with no conceptual challenges, making it easier than average but not trivial since students must recall the correct z-value and formula structure.
Spec	5.05d Confidence intervals: using normal distribution

1 In a survey of 1000 randomly chosen adults, 605 said that they used email. Calculate a \(90 \%\) confidence interval for the proportion of adults in the whole population who use email.

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Question 1:

Answer	Marks	Guidance
Answer/Working	Marks	Guidance
\(0.605 \pm z \times \sqrt{\frac{0.605 \times (1-0.605)}{1000}}\)	M1
\(z = 1.645\) seen	B1	Allow \([0.58, 0.63]\)
\([0.580, 0.630]\)	A1 [3]	Allow any brackets

## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $0.605 \pm z \times \sqrt{\frac{0.605 \times (1-0.605)}{1000}}$ | M1 | |
| $z = 1.645$ seen | B1 | Allow $[0.58, 0.63]$ |
| $[0.580, 0.630]$ | A1 [3] | Allow any brackets |

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1 In a survey of 1000 randomly chosen adults, 605 said that they used email. Calculate a $90 \%$ confidence interval for the proportion of adults in the whole population who use email.

\hfill \mbox{\textit{CAIE S2 2010 Q1 [3]}}

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Q1 3 Q2 5 Q3 7 Q4 7 Q5 8 Q6 9 Q7 11