Assignment 1.docx

Stochastic Modelling Assignment 1 (17th March 2019) 1. The proportion of adults living in a small town who are college graduates is estimated to be 0.3 (= π). To test this hypothesis a random sample of 15 adults is selected. If the number of college graduates in the sample is anywhere from 2 to 7, the null hypothesis π = 0.3 is accepted; otherwise it is concluded that π ≠ 0.3. Evaluate size of type I error. Also calculate probability of type II error for the alternatives π = 0.2 and π = 0.4. 2. In a large experiment to determine the success of a new drug, 400 patients with a certain disease are to be given the drug. If more than 300 but less than 340 patients are cured, it is concluded that the drug is 80 % effective. Calculate the probability of concluding that drug is not 80% effective while in reality it is effective. What is the probability of committing type II error if the new drug is only 70% effective? 3. Let X be N(μ, σ2=100). To test H0: μ = 60 against H1: μ > 60, use a rejection region of the form x  c. Determine the approximate sample size as well as the value of ‘c’ so that the probability of committing type I error is 0.05 and the probability of committing type II error when μ = 65 is also 0.05.