A college has 152 assistant professors, 127 associate professors, and 208 full professors. The college administration is investigating the amount of time these faculty members spend in meetings in a semester. Random samples of 40 assistant professors, 40 associate professors, and 50 full professors were asked to keep records of time spent in meetings during a semester. The sample means were 27.6 hours for assistant professors, 39.2 hours for associate professors, and 43.3 hours for full professors. The sample standard deviations were 7.1 hours for assistant professors, 9.9 hours for associate professors, and 12.3 hours for full professors.

a. Find a 90% confidence interval for the mean time spent in meetings by full professors at this college during the semester.

b. Using an unbiased estimation procedure, estimate the mean time spent in meetings by all faculty members at this college during the semester.

c. Find 90% and 95% confidence intervals for the mean time spent in meetings by all faculty members at this college during the semester