Question 1 - A-Level Maths

CAIE S2 2017 March — Question 1 4 marks

Exam Board	CAIE
Module	S2 (Statistics 2)
Year	2017
Session	March
Marks	4
Paper	Download PDF ↗
Mark scheme	Download PDF ↗
Topic	Confidence intervals
Type	Calculate CI for proportion
Difficulty	Moderate -0.8 This is a straightforward application of the standard confidence interval formula for a proportion with no complications. Students need only recall the formula, substitute values (p̂ = 36/120 = 0.3, n = 120, z = 1.645), and calculate—purely routine with no problem-solving or conceptual challenge beyond basic recall.
Spec	5.05d Confidence intervals: using normal distribution

1 In a survey, 36 out of 120 randomly selected voters in Hungton said that if there were an election next week they would vote for the Alpha party. Calculate an approximate \(90 \%\) confidence interval for the proportion of voters in Hungton who would vote for the Alpha party.

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Question 1:

Answer	Marks	Guidance
Answer	Marks	Guidance
\(\text{Var}(P_s) = \frac{0.3(1-0.3)}{120}\) \((= 0.00175)\)	M1	Attempt correct values in correct formula
\(0.3 \pm z\sqrt{0.00175}\)	M1	Must be a \(z\)-value, not a prob
\(z = 1.645\)	B1
\(\text{CI} = 0.231\) to \(0.369\) (3 sf)	A1

## Question 1:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\text{Var}(P_s) = \frac{0.3(1-0.3)}{120}$ $(= 0.00175)$ | M1 | Attempt correct values in correct formula |
| $0.3 \pm z\sqrt{0.00175}$ | M1 | Must be a $z$-value, not a prob |
| $z = 1.645$ | B1 | |
| $\text{CI} = 0.231$ to $0.369$ (3 sf) | A1 | |

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1 In a survey, 36 out of 120 randomly selected voters in Hungton said that if there were an election next week they would vote for the Alpha party. Calculate an approximate $90 \%$ confidence interval for the proportion of voters in Hungton who would vote for the Alpha party.\\

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

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