1. [20 pt.] The American Society for Quality (ASQ) conducted a salary survey of all its members. ASQ. members work in all areas of manufacturing and service-related institutions, with a common theme of an interest in quality. Two job titles are black belt and green belt. Descriptive statistics concerning salaries for these two job titles are given in the following table. Job Title Sample size Mean STD Green belt 26 74,173 23,399 Black belt 121 93,946 21,166 (a) Using a 0.05 level of significance, is there a difference in the variability of salaries between black belts and green belts? State null and alternative hypotheses to test it and make your conclusion. (Assume that 1 and 62 are the population standard deviations of salaries of the green belt and the black belt, respectively.) (b) State null and alternative hypotheses to test whether the mean salary of black belts greater than the mean salary of green belts. (Assume that u, and 2 are the means of salaries of green belt and black belt, respectively.) (c) Using a 0.05 level of significance, is the mean salary of black belts greater than the mean salary of green belts? Show the work: i) test statistic, ii) critical value, and iii) decision