1、(20%) A vendor of milk products produces and sells low-fat dry milk to a company that uses it to produce baby formula. In order to determine the fat content of the milk, both the company and the vendor take a sample from each lot and test it for fat content in percent. Ten sets of paired test results

Let $\mu_D = \mu_X - \mu_Y$ denote the mean of the differences between X and Y. Test H0: $\mu_D = \mu_X - \mu_Y = 0$ against H1: $\mu_D = \mu_X - \mu_Y > 0$ using t-test for the differences. Let $\alpha = 0.05$. (All values are rounded to the third decimal place.) (Hints: t_0.95(9) = 1.833; t_0.975(9) = 2.262; t_0.95(10) = 1.812; t_0.975(10) = 2.228, where P(t < t1-α(r)) = 1 - α for a t random variable with a freedom r)