Question 1 - A-Level Maths

CAIE S2 2023 June — Question 1 3 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2023
Session	June
Marks	3
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Confidence intervals
Type	Calculate CI for proportion
Difficulty	Moderate -0.5 This is a straightforward application of the confidence interval formula for a proportion with given sample size, proportion, and confidence level. It requires only direct substitution into a standard formula (p ± z√(p(1-p)/n)) with no conceptual challenges or multi-step reasoning, making it slightly easier than average.
Spec	5.05d Confidence intervals: using normal distribution

1 In a survey of 200 randomly chosen students from a certain college, 23\% of the students said that they owned a car. Calculate an approximate \(93 \%\) confidence interval for the proportion of students from the college who own a car.

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Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(0.23 \pm z \times \sqrt{\dfrac{0.23 \times (1-0.23)}{200}}\)	M1	Expression of correct form. Any \(z\), but \(z = 0.8328\) scores B0M0.
\(z = 1.811\) or \(1.812\)	B1
\(0.176\) to \(0.284\) (3 sf)	A1	Must be an interval.
Total: 3

**Question 1:**

| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.23 \pm z \times \sqrt{\dfrac{0.23 \times (1-0.23)}{200}}$ | M1 | Expression of correct form. Any $z$, but $z = 0.8328$ scores B0M0. |
| $z = 1.811$ or $1.812$ | B1 | |
| $0.176$ to $0.284$ (3 sf) | A1 | Must be an interval. |
| **Total: 3** | | |

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1 In a survey of 200 randomly chosen students from a certain college, 23\% of the students said that they owned a car.

Calculate an approximate $93 \%$ confidence interval for the proportion of students from the college who own a car.\\

\hfill \mbox{\textit{CAIE S2 2023 Q1 [3]}}

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