A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2025 · Q68 Marks

Nikki is investigating the views of students at her school about the school sports facilities. She plans to give a survey to a sample of students. Nikki's friend says, “This survey is about sports facilities, so you should choose a sample of students from the school sports teams.”

(a)State, with a reason, whether you agree with Nikki's friend.[1]
(b)Nikki chooses an appropriate random sample of 60 students. She finds that 45 of these students think that the sports facilities are good. Calculate an approximate 95% confidence interval for the proportion of students who think that the sports facilities are good.[3]
(c)For a different investigation, Nikki uses another large random sample to calculate a 99% confidence interval and an x% confidence interval. The width of the 99% confidence interval is double the width of the x% confidence interval. Calculate the value of x.[4]

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2025). The mark or mark type is shown in brackets.

[B1] e.g. No. The views of students in sports may be different from other students. No and any sensible reason for disagree. Allow just No, because biased (or not random) or not representative.
[M1] p̂ ± z * √(p̂(1-p̂)/n) Any z.
[B1] z = 1.96
[A1] 0.640 to 0.860 (3 sf) or 0.64 to 0.86 Must be an interval. Mark at the most accurate.
[M1] Φ-1(0.995) [= 2.574 to 2.579] Allow Φ-1(0.99).
[M1] Φ('2.576' ÷ 2) [= Φ(‘1.288') = 0.901 to 0.9015] FT their 2.576.
[M1] '0.9012' - (1 – '0.9012') OE.
[A1] [= 0.802 to 0.803] ⇒ x = 80.2 to 80.3 or x ≈ 80 Allow x = 80%.

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