CAIE A-Level Mathematics 6.5.1 Hypothesis-Test Foundations

CAIE A-Level Mathematics 6.5.1 Hypothesis-Test Foundations
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise defining null and alternative hypotheses, choosing one or two tails and using significance levels, test statistics and rejection regions to reach contextual conclusions.

How this is tested

  • write H₀ with equality and direct H₁ toward the claimed increase, decrease or difference
  • choose a rejection region whose null probability does not exceed the significance level
  • compare the observation with that region and conclude in terms of evidence for the claim

Question 2(a)

[Maximum number: 1]

A researcher is investigating whether the proportion of families who do not own a car in his town is different from the proportion of the population in the whole country, which is 10.1%. He takes a large random sample of families in his town and finds the proportion of families that do not own a car.

Explain why a two-tailed test is appropriate in this context.