An exam is given to all senior high school students, the standard deviation for all the students is given as 30. The average score for 50 students on the exam is 540. Assume the means to be measured to any degree of accuracy (assume that scores are Gaussian distributed). (a) Find the 90% confidence interval (CI) for the average score of all students taking the exam. (b) Find the prediction interval for the score of the next student chosen at random (not one of the original so students). TTT Arial 3 (121) T.5.15 QUESTION 2 Given the following weights, find the 98% CI for the variance of the weights: 9 10 00 7 5 3 1 4 6 2 37 34 36 35 42 40 38 34 41 34 TT T Arial 3 (12pt) TE 25 QUESTION 3 According to a newspaper only 20% of 280 adults polled by telephone say they think going to Mars is a good idea for the world. Find the 90% ci for the proportion of adults who think that going to Mars is a good investment for the world. w TT T Arial 3 (12pt) T..E cs QUESTION 4 A new type of rope has a mean breaking strength of 15 kilograms with a standard deviation of 0.5 kilogram. To test the hypothesis, a random sample of 50 lines are tested and the average breaking strength is found to be 14.8 kilograms. (a) Test the hypothesis, at the 0.01 level of significane the the mean is that p - 15 kilograms against the alternative that p