1 (8 points, each 2point) (1) ( ) For a fixed sample size, Type-II error)( decreases if Type-I error)( increases. (2) ( ) The normality assumption of the monitoring statistic (quality characteristic) is one of the main assumptions of Shewhart control charts. (3) ( ) In Shewhart control charts, if the Shewhart multiplier (k) increases, the percentage of nonconforming parts always decreases. (4) ( ) If a quality characteristic (X) is NOT normally distributed, Type-I error corresponding to a 3-sigma control chart is either larger or smaller than 0.0027. Problem 2 (points 22) One of the students in the department of Industrial and Operations Engineering at the University of Michigan claims that his classmates have the average IQ greater than 120. To prove his statement, he gives an IQ test to 15 randomly selected students in the department. Previous study indicates that the standard deviation of IQ for students' population is 6. Based on the following summary data from the sample, answer the questions below. ?? = 1890 15 ?=1 (a) State the hypothesis that you think should be tested (4 points). (b) Test your hypothesis in part (a) using = 0.01 and draw conclusion (6 points)