1 For each of the following situations, say what unit might be used as psu. Do y
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1 For each of the following situations, say what unit might be used as psu. Do you believe there would be a strong clustering effect? Would you sample psus with equal or unequal probabilities? a You want to estimate the percentage of patients of U.S. Air Force optometrists and ophthalmologists who wear contact lenses. b Human taeniasis is acquired by ingesting larvae of the pork tapeworm in inad equately cooked pork. You have been asked to design a survey to estimate the percentage of inhabitants of a village who have taeniasis. A medical examination is required to diagnose the condition You wish to estimate the total number of cows and heifers on all Ontario dairy farms; in addition, you would like to find estimates of the birth rate and stillbirth rate. c d You want to estimate the percentages of undergraduate students at U.S. universities who are registered to vote, and who are affiliated with each political party A trap hauled from a fishing boat has a limit of 30 crabs guided bus tours of the Grand Canyon rim area. Tour g e A fishe ries agency is interested in the distribution of carapace width of sm ow crabs. You wish to conduct a customer satisfaction survey of persons who have taken roups range in size from 8 to 44 persons.Explanation / Answer
Introduction: To reduce cost and time of sampling, we often resort to Cluster Sampling. In Cluster sampling we divide the entire population into Blocks (called Primary Sampling Units(PSU)) and then in each PSU we have the actual sampling unit (individuals) called Secondary Sampling Units. We assign equal/unequal probability of selection to each PSU and select few PSUs. Once the PSU are selected we again sample (usually a SRSWOR) for SSU within the selected PSUs.
Problem: We want to suggest for each sample survey in queston, what will be a likely choice for PSU. If we will assign equal/unequal probability of selection to each PSU and if there will be clustering effect (if clusters are not a true representative of the entire population)
Solution:
(a) We want to estimate the number of paitents of US Air Force (Optometrists and opthalmologists) who wear contact lenses.
A natural choice of PSU will be dividing the US Air Force total personnel into geographical regions say each USA state and have another PSU for foreign land postings of personnel. So PSU will be graphical zones. We will assign higher probability to the PSUs which are nearer to our testing lab so that we minimize time and cost.
There will be a very slight clustering effect because possibly the foreign posted personnel will not be mostly using contact lenses (they will be screend not to have any visual limitation). So that PSU will have a different count of Contact lense user than other groups. However since this is only applicable for one cluster so it is not major.
(c) Similar to (a), here the PSU should be geographical zones in Ontario. Each zone (Locality/village/town) becomes a PSU and the farms within the locality becomes the SSU. We will assign equal probability to all PSU because afterall its within Ontario and so cost will not increase due to inclusion of any particular farm. Since the geographical region is Ontario only hence all cows face similar climatic conditions, so if we assume that they all get similar level of farming care then we can comment that there will be not much clustering effect.
(d) Similar to above, again the political/regional states of USA will be a good choice of PSU and the students of universties within each state the SSU. We can assign equal probability to each PSU because each state in USA is almost equally politically active and hence is little chance of clustering effect.
(f) We can take PSU to be the regional states, but will laways assign unequal probability to the PSUs, because the chances of getting a SSU (Individual whoc have taken the guided tour) in a state surrounding the Grand Canyon area is much more than a state like Washington. So we will assign a 0.1 to each of the 5 surrounding state and 0.1 to state containing Grand Canyon and divide the remaining 0.4 probability to the remaining states. Clsutering effect will creep in because individuals located close to Grand Canyon will possibly give a good feedback of their own state than tourists from other states.
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