Problem Behavioral researchers have developed an index designed to measure manage- rial success. The index (measured on a 100-point scale) is based on the manager's length of time in the organization and his or her level within the firm; the higher the index, the more successful the manager. Suppose a researcher wants to compare the average suc- cess index for two groups of managers at a large manufacturing plant. Managers in group 1 engage in a high volume of interactions with people outside the manager's work unit. (Such interactions include phone and face-to-face meetings with customers and suppliers, outside meetings, and public relations work.) Managers in group 2 rarely interact with people outside their work unit. Independent random samples of 12 and 15 managers are selected from groups 1 and 2, respectively, and the success index of each is recorded. The results of the study are given in Table 7.2. a. Use the data in the table to estimate the true mean difference between the success indexes of managers in the two groups. Use a 95% confidence interval. b. Interpret the interval, part a. c. What assumptions must be made in order that the estimate be valid? Are they rea- sonably satisfied? Table 7.2 Managerial Success Indexes for Two Groups of Managers Group 1 Group 2 Interaction with Outsiders Few Interactions 65 58 78 60 68 69 62 53 36 34 56 50 66 70 53 71 63 63 42 57 46 68 48 42 52 53 43Managerial Success Indexes for Two Groups of Managers iroup 1 (interaction with outsiders) Group 2 (few interactions) t-Test: Paired Two Sample for Means 65 62 58 53 Group 1 (interaction with outsiders) Group 2 (few interactions) 78 36 Mean 52.26666667 49.46666667 60 34 Variance 766.0666667 87.12380952 68 56 Observations 15 15 69 50 Pearson Correlation 0.034873869 66 42 Hypothesized Mean Difference 100 70 57 df 14 53 46 t Stat -13.02639011 71 68 P(T