CAIE A-Level Mathematics 6.5.2 Binomial and Poisson Hypothesis Tests

CAIE A-Level Mathematics 6.5.2 Binomial and Poisson Hypothesis Tests
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise testing a proportion or event rate from one observation using exact binomial or Poisson probabilities, or a justified normal approximation with continuity correction.

How this is tested

  • state H₀ and H₁ for p or λ and select the lower, upper or two-tailed event
  • calculate the observed tail directly from B(n, p) or Po(λ), including all equally extreme values
  • when justified, use the matching normal mean and variance with continuity correction before testing

Question 3(a)

[Maximum number: 6]

A certain website receives an average of μ\mu hits per hour. In the past the value of μ\mu was 14.4. After making some improvements, the owner of the website wishes to test whether the value of μ\mu has increased. He chooses a 10 -minute period at random and finds that there were 6 hits during this period. You may assume that the number of hits the website receives in any given time period follows a Poisson distribution.

Carry out the test at the 2.5% significance level.