A study is being conducted to compare the average training time for two groups of airport security personnel: those who work for the federal government and those employed by private security companies. In a random sample of government employed security personnel, average training time was 68.2 hours, with a sample standard deviation of 10.4 hours. In a random sample of privately employed security personnel, training time was 65.4 hours, with a sample standard deviation of 12.3 hours. Would these sample results be sufficient to reject a “no difference in average training times” null hypothesis at the 5% significance level, if the samples consisted of 

a. 12 government personnel and 16 private company personnel. Assume that the population distributions are normal and have equal standard deviations. 

b. 120 government personnel and 160 private company personnel.