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Refer to the Periodic Table produced by the National Institute of Standards and Technology (NIST) in 2003. This Periodic Table displays 114 elements, along with their corresponding atomic numbers and atomic weights. Notice that the atomic weight of the elements generally increases with the atomic number of the elements. Thus, the first element listed, Hydrogen, with an atomic number of 1, has the lowest atomic weight of 1.01 grams per mole -- and the last element listed, Ununhexium, with an atomic number of 116, has the highest atomic weight of 292 grams per mole. In order to practice selecting different types of samples and to compare the performance of different types of samples, we are going to consider our Population of interest to be all of the elements shown on the NIST 2003 Periodic Table (thus, N = 114) and the variable of interest is atomic weight. Let’s assume that we are interested in selecting samples from this population in order to estimate the population mean atomic weight. The true mean atomic weight of the 114 elements on the NIST Periodic Table is 141.09 grams per mole. SAMPLING:Select a simple random sample of 25 elements. Sample without replacement. Use a seed of 1967 and generate the numbers one at a time with your calculator, not as a list. What is the mean atomic weight for the 25 sampled elements? (2 points)Select a 1 in 5 systematic sample of elements (note that this sample will be less than 25 elements). Use a seed of 1985. What is the mean atomic weight for the sampled elements? (2 points)To select a stratified sample of 25 elements, without replacement, we could divide the table into 4 strata: Solid, Liquid, Gas, and Artificial. Note that on this table there are 77 Solids, 2 Liquids, 11 Gases, and 24 Artificial elements. We are going to sample 17 Solids, 1 Liquid, 2 Gases, and 5 Artificial elements.Why does it make sense to sample 17 of the solids? (1 point)Use a seed of 1972 for solids, a seed of 1977 for liquids, a seed of 1990 for gases, and a seed of 2015 for artificial elements.What is the mean atomic weight for the 25 sampled elements? (2 points)Select a cluster sample of elements. Use the columns of elements as the clusters. Thus there are 18 clusters. Randomly select 4 clusters. Use the seed 33. Explain why it makes sense to use the columns as clusters, but it does not make sense to use the rows as clusters. (2 points)What is the mean atomic weight for the sampled elements? (2 points)OTHER SAMPLING QUESTIONS:A farmer has four orchards of apple trees which are located at different locations on his farm. Each orchard has 200 apple trees. He wishes to find out whether the apple trees are infested with a certain type of insect. If this is so, he would hire a crew to spray his trees. Instead of examining all 800 trees, he decides to select a sample of trees and just examine these. There are three proposed sampling plans described below: (1 point)Plan 1: Randomly select 100 trees from the 800 trees. Plan 2: Randomly select 20 trees from each of the 4 orchards.Plan 3: Randomly select 1 orchard from the 4 orchards, and then select all trees from the selected orchard. For each of the above plans, identify the type of sampling method being proposed (simple random sample, stratified random sample, cluster sample, systematic sample). Plan 1: ____________________________________________________ Plan 2: ____________________________________________________ Plan 3: ____________________________________________________There are 16 first class passengers scheduled on a flight. In addition to the usual security screening, 4 of the passengers will be subjected to a more complete search. Here is the first class passenger list, denoted by which Section that the passenger is seated in. (1 point each)Section 1 Section 2 Section 3 Section 4 1. Bergman5. DeLara 9. Frongillo 13. Swafford 2. Cox6. Forrester 10. Roufaiel 14. Clancy 3. Fontana 7. Rabkin 11. Castillo 15. Febo 4. Perl8. Burkhauser 12. Dugan 16. LePage (a) Select a simple random sample of 4 passengers. Use a seed of 845. Selected passengers: (b) Select a cluster sample of 4 passengers. Use the Sections of passengers as clusters. Use a seed of 332. Selected passengers: (c) Select a 1-in-4 systematic sample of 4 passengers. Use a seed of 75.Selected passengers: ................
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