A study of the career paths of hotel general managers sent questionnaires to an SRS of 280 hotels belonging to major U. S. hotel chains. There were 167 responses. The average time these 167 general managers had spent with their current company was 11.77 years. (Take it as known that the standard deviation of time with the company for all general managers is 4.5 years.) (a) Find the margin of error for a 90% confidence interval to estimate the mean time a general manager had spent with their current company: years (b) Find the margin of error for a 99% confidence interval to estimate the mean time a general manager had spent with their current company: years (c) In general, increasing the confidence level the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)