Small manufactured goods are often gathered into large batches, called lots, for purposes of handling and shipping. Random sampling is commonly used to evaluate the quality of items in a given lot. Sup-pose an inspector selects a random sample of 20 items from a lot of 1000 items. a. Before evaluating the 20 items, the inspector decides that a sample of size 30 should be used in-stead. If the inspector obtains a second random sample of size 10 from the remaining 980 items, can the two samples combined be validly considered a random sample of 30 from the lot? Explain your reasoning. b. Suppose the inspector decides that only 15 items must be tested. Describe a method by which a valid random sample of 15 from the lot can be formed from the 20 items already selected.