CIE A level Math -Probability & Statistics 2: 6.5 Hypothesis tests :probabilities of making Type I and Type II errors: Exam Style Questions Paper 6


 In the past, Arvinder has found that the mean time for his journey to work is 35.2 minutes. He tries a different route to work, hoping that this will reduce his journey time. Arvinder decides to take a random sample of 25 journeys using the new route. If the sample mean is less than 34.7 minutes he will conclude that the new route is quicker. Assume that, for the new route, the journey time has a normal distribution with standard deviation 5.6 minutes.

     (i) Find the probability that a Type I error occurs. [4]

     (ii) Arvinder finds that the sample mean is 34.5 minutes. Explain briefly why it is impossible for him to make a Type II error. [1]