CAIE A-Level Mathematics 6.4.8 Proportion confidence intervals

CAIE A-Level Mathematics 6.4.8 Proportion confidence intervals
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise forming approximate confidence intervals for population proportions and using interval limits to interpret claims.

How this is tested

  • calculate a proportion interval using p̂ ± z√(p̂(1−p̂)/n) from a large sample
  • set up equations from interval width or a limit to find z, p̂, or the confidence level
  • use whether a claimed proportion lies in the interval to comment on the claim

Question 6(c)

[Maximum number: 3]

A manufacturer of cell phones claims that 25% of students own a Pumpkin phone. Jeyeraj thinks that the proportion of students at his large college who own a Pumpkin phone is less than 25%. He plans to test the manufacturer's claim. He chooses a random sample of 30 students at his college. If the number of students who own a Pumpkin phone is less than 5, Jeyeraj will reject the manufacturer's claim.

Calculate an approximate 95% confidence interval for the proportion of students at Florence's

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Figure for Question 6(c) — CAIE A-Level Mathematics

Florence's college, in a random sample of 40 students, it was found that 5 own a Pumpkin phone. college who own a Pumpkin phone. -

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