The Human Resources (HR) office of a company is responsible for managing the cost of providing health care benefits to employees. HR managers are concerned that health care costs differ among several departments: administration, clerical, manufacturing, information technology (IT), and sales. Staff selected a sample of 15 employees of each type and carefully assembled a summary of health care costs for each.
(a) Plot the data. From your visual inspection of the plot, do you think there are statistically significant differences among these five departments?
(b) Fit a multiple regression of health care cost on four dummy variables that identify employees in administration, clerical, IT, and manufacturing. Interpret the estimated intercept and slopes.
(c) Does a statistical test agree with your visual impression? Test the null hypothesis that costs are the same in the four departments.
(d) Do these data meet the conditions required for an ANOVA?
(e) Assuming the data are suitable for ANOVA, is there a statistically significant difference between the costs in the two most costly departments?
(f) Nationally, the cost of supplying health benefits averages $4,500. Assuming these data are suitable for ANOVA, should the HR managers conclude that any of these departments have particularly high or low costs?