CAIE A-Level Mathematics 6.5.5 Type I and Type II Errors

CAIE A-Level Mathematics 6.5.5 Type I and Type II Errors
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise calculating Type I and Type II error probabilities from a stated rejection region under the null or a specified alternative binomial, Poisson or normal model.

How this is tested

  • calculate Type I error as the probability of the rejection region when H₀ is true
  • calculate Type II error as the probability of the acceptance region under the stated alternative
  • retain the same critical boundary but substitute the null or alternative model required by the error

Question 6(c)

[Maximum number: 5]

The weekly profit, in dollars, made by a certain firm has a normal distribution. In the past, the weekly profit had the distribution N(736,262)\mathrm{N}\left(736,26^{2}\right). Following a change in management, the mean weekly profit for 35 randomly chosen weeks is $ 725.

Given that the mean weekly profit is now in fact $ 718, find the probability of a Type II error.