Independent random samples are taken from the output of two machines on a production line. The weight of each item is of interest. From the first ma¬

chine, a sample of size 36 is taken, with sample mean weight of 120 grams and a sample variance of 4 grams. From the second machine, a sample of size 64 is taken, with a sample mean weight of 130 grams and a sample variance of 5 grams. It is assumed that the weights of items from the first machine are normally distributed with mean px and variance cr2, and that the weights of items from the second machine are normally distributed with mean p2 and variance cr2 (that is, the variances are assumed to be equal). Find a 99 percent confidence interval for the difference in population means, p\ — p2.