4. The manager of a car rental firm claims that the average kilometers traveled per day by each of its cars rented in Ankara is differs from 70km. To justify this claim they collected a random sample of 25 cars. The sample yields an average of 85.5kms per day and the population standard deviation is known as 19.3kms per day. It is assumed that the kilometers traveled is normally distributed. a) (5 pts) Construct a hypothesis test that can be used to help the manager test their claim. State your null hypothesis and alternative hypothesis in terms of the relevant population parameter. b) (5 pts) Test the hypotheses constructed in part (a) using a significance level of 0.01. State your conclusion also in words. Use critical value approach. c) (5 pts) Suppose that in reality, the average traveled distance is 82 kilometers. Calculate the type 2 error probability using a significance level of 0.01. d) (5 pts) Find the sample size required to detect an actual average traveled distance of 82 kilometers with probability 0.95 when the significance level is set at 0.01.