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CAIE A-Level Mathematics 6.4.7 Confidence Intervals for a Population Mean

Practise constructing and interpreting confidence intervals for a population mean using a known variance or large sample, an appropriate z-value and the standard error.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • select the two-tailed standard-normal critical value for the stated confidence level
  • calculate the interval as x̄ ± zσ/√n, using an estimated deviation for a large sample
  • interpret confidence level, margin of error or interval width without treating μ as random

6.4.7—Mean confidence intervals question 1

[Maximum number: 3]

Batteries of type A are known to have a mean life of 150 hours. It is required to test whether a new type of battery, type B, has a shorter mean life than type A batteries.

Calculate a 94% confidence interval for the population mean life of type B batteries.

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