Jose is a human resources executive for a technology company He is deciding between two types of plans for vacation allowance for the employees of the company Unlimited and Traditional Jose wants to estimate for workers in the tech industry the difference between the yearly mean number of vacation days taken by workers with an Unlimited plan and the yearly mean number of vacation days taken by workers with a Traditional plan Jose surveys a random sample of 17 workers who have the Unlimited plan and a random sample of 16 workers who have the Traditional plan These samples are chosen independently For each worker he records the number of vacation days taken last year For the workers with an Unlimited plan the sample mean is 17 6 with a sample variance of 44 6 For the workers with a Traditional plan the sample mean is 15 9 with a sample variance of 9 7 Assume that the two populations of vacation days taken are approximately normally distributed Let u be the population mean number of vacation days taken by workers with an Unlimited plan Let be the population mean number of vacation days taken by workers with a Traditional plan Construct a 90 confidence interval for the difference Then find the lower and upper limit of the 90 confidence interval Carry your intermediate computations to three or more decimal places Round your answers to two or more decimal places If necessary consult a list of formulas Lower limit Upper limit X S