Question 1 - A-Level Maths

CAIE S2 2017 June — Question 1 4 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2017
Session	June
Marks	4
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 p̂ ± 1.96√(p̂(1-p̂)/n) with no complications, making it easier than average and typical of routine S2 questions.
Spec	2.05a Hypothesis testing language: null, alternative, p-value, significance 2.05d Sample mean as random variable

1 In a survey of 2000 randomly chosen adults, 1602 said that they owned a smartphone. Calculate an approximate \(95 \%\) confidence interval for the proportion of adults in the whole population who own a smartphone.

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Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(\frac{0.801 \times (1-0.801)}{2000}\) \((= 0.0000797)\)	M1
\(0.801 \pm z \times \sqrt{0.0000797}\)	M1	Allow any \(z\)-value
\(z = 1.96\)	B1
\(0.784\) to \(0.818\) (3 sf)	A1	As final answer. Must be an interval. Allow 0.783 to 0.819
Total:	4

## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{0.801 \times (1-0.801)}{2000}$ $(= 0.0000797)$ | M1 | |
| $0.801 \pm z \times \sqrt{0.0000797}$ | M1 | Allow any $z$-value |
| $z = 1.96$ | B1 | |
| $0.784$ to $0.818$ (3 sf) | A1 | As final answer. Must be an interval. Allow 0.783 to 0.819 |
| **Total:** | **4** | |

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1 In a survey of 2000 randomly chosen adults, 1602 said that they owned a smartphone. Calculate an approximate $95 \%$ confidence interval for the proportion of adults in the whole population who own a smartphone.\\

\hfill \mbox{\textit{CAIE S2 2017 Q1 [4]}}

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Q1 4 Q2 5 Q3 8 Q4 7 Q5 8 Q6 9 Q7 9