22 7. A manufacturer has a machine that produces lollipop sticks. The length of a lollipop stick produced by the machine is normally distributed with unknown mean μ and standard deviation 0.2 Farhan believes that the machine is not working properly and the mean length of the lollipop sticks has decreased. He takes a random sample of size n to test, at the 1% level of significance, the hypotheses H0: μ = 15 H1: μ < 15 (a) Write down the size of this test. (1) Given that the actual value of μ is 14.9 (b) (i) calculate the minimum value of n such that the probability of a Type II error is less than 0.05 Show your working clearly. (6) (ii) Farhan uses the same sample size, n, but now carries out the test at a 5% level of significance. Without doing any further calculations, state how this would affect the probability of a Type II error. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________