CAIE A-Level Mathematics 6.5.4 Hypothesis tests

CAIE A-Level Mathematics 6.5.4 Hypothesis tests
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise interpreting Type I and Type II errors from the test decision, including when each error is possible or impossible.

How this is tested

  • explain a Type I error as rejecting H0 when the original claim is actually true
  • decide whether Type I or Type II errors are possible from whether H0 was rejected
  • state the Type I error probability from the significance level or rejection region

Question 3(b)

[Maximum number: 2]

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.

Explain whether it is possible that a Type I error or a Type II error or both may have been made in carrying out the test.