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CAIE A-Level Mathematics 6.4.1 Samples and Populations

Practise distinguishing samples from populations, explaining why a census may be impractical or destructive and specifying random selection that avoids bias and duplication.

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • identify the full population and the measured sample before interpreting a statistic or estimate
  • justify sampling by cost, time, population size or destructive testing in the stated context
  • number every member and use valid random numbers, rejecting out-of-range values and repeats

6.4.1—Samples and populations question 1

[Maximum number: 1]

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.

Give a reason for using a sample rather than the whole population in carrying out this test.

A random sample of 120 type B batteries are tested and it is found that their mean life is 147 hours, and an unbiased estimate of the population variance is 225 hours 2^{2}.

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