Behavioral researchers have developed an index designed to measure managerial 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. A researcher wants to compare the average success 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 their work unit, while 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 and the success index of each recorded. In group 1 the mean is 65.33 and the standard deviation is 6.61. In group 2 the mean is 49.47 and the standard deviation is 9.33. Test the null that there is no difference versus the alternative that there is a difference. Use alpha =0.05.