The manufacturers of Good-O use two different types of machines to fill their 25 kg packs of dried dog food. On the basis of random samples of size 12 and 14 from output from machines 1 and 2 respectively, the mean and standard deviation of the weight of the packs of dog food produced were found to be 24.570 kg and 0.361 kg for machine 1 and 25.068 kg and 0.346 kg for machine 2. Hence, under the usual assumptions, determine a 98% confidence interval for the difference between the average weight of the output produced by machine 1 and by machine 2. Construct the interval as the average weight of machine 1 minus machine 2, stating only the lower limit of the interval correct to3 decimal places.