Exercise 1 (9 marks) A random sample of 100 recorded deaths in the United States during the past year showed an average life span of 71.8 years. a) Assuming a population standard deviation of 8.9 years. does this seem to indicate that the mean life span today is at most 70 years? bj Verify your work in part (a) by using an appropriate confidence interval. (Don't forget to state the appropriate level of confidence} Exercise 2 (4 marks) The manufacturer of a heavy-duty cooling fan claims that the mean lifetime of these fans under severe conditions is greater than 6 months. For each of the following situations. determine whether the decision was correct. a type I error occurred. or a type II error occurred. a} The claim is true. and H" is rejected. b} The claim is false. and Ht, is rejected. c) The claim is true. and H" is not rejected. at The claim is false. and H" is not rejected. Exercise 5 (9 marks) Suppose that we wish to determine whether the opinions of the voting residents of the province of Ontario concerning a new tax reform are independent of their levels of income at a 0.05 significance level. A random sample of 1000 registered voters from the province of Ontario are classified as to whether they are in a low, medium, or high income bracket and whether or not they favor a new tax reform. Complete the relevant test. Income Level Tax Reform Low Medium High For 182 213 203 Against 154 138 110