1. From a population of automobile assembly workers, a sample of 100 are randomly selected for a study of the effects of a new training program on productivity. At the beginning of the program, their mean productivity score over the previous year was 35 with a standard deviation of 5. At the end of the program, their mean productivity score was 44 with a standard deviation of 8. The distribution of productivity score is assumed to be normal. (0.5 pt each, 1 pt in total)
   1. What test would you use to answer the question "was the new training program more effective on productivity?"

b. Productivity scores for the entire factory over the previous year was 29 with a standard deviation of 4. What test would you use to answer the question "To what extent were the workers chosen for this study representative of the workers in the entire factory?"