A manufacturing company packages shipments in either large or small boxes. A random sample of 40 shipments that are packaged in large boxes is found to have a mean of 15 pounds and a standard deviation of 2 point 8 pounds. A separate random sample of 50 shipments that are packaged in small boxes is found to have a mean of 10 pounds and a standard deviation of 1 point 5 pounds. The manager would like to know if the data provide convincing evidence that the true mean weight of all shipments that are packaged in small boxes is less than the true mean weight of all shipments that are packaged in large boxes. The manager tests ratio of cap h sub 0 to mu sub cap s minus mu sub cap l is equal to 0 , ratio of cap h sub A to mu sub cap s minus mu sub cap l is less than 0 , where mu sub cap l is equal to the true mean weight of all shipments that are packaged in large boxes and mu sub cap s is equal to the true mean weight of all shipments that are packaged in small boxes. The conditions for inference have been met. What are the values of the test statistic and cap p -value for a t - test about a difference in means? Use the t -table and the z -table.