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# Clustered and stratified sampling

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A. Design effects are used to evaluate the precision of statistics for different sample design.
Is the design effect of a clustered element sample likely to be larger or smaller than one?
Is the design effect of a stratified element sample likely to be larger or smaller than one?
In a single stage clustered sample, if within a cluster a variable has nearly the same value for all elements within the cluster, what value will the intraclass correlation be close to?
For a single-stage clustered sample, the intraclass correlation for a key variable is 0.016 and the cluster size is 10. Calculate the design effect for the mean of that key variable.
What does the design effect in part 4 mean?

B. A medical practice has record for N=900 patients. A simple random sample of n=300 was selected, and 210 of the sample patients had private health insurance.
1. Estimate the percentage of patients with private health insurance and the standard error of this estimate.
2. Calculate a 95% confidence interval for the population percentage.
3. The study is to be repeated in another medical practice that has N=1000 patients. A standard error of 2.5 percentage points for the sample percentage of patients with private health insurance is required. What sample size is needed for a simple random sample to achieve this level of precision? For planning purposes, assume that the population percentage is 50%.

C. A two-stage cluster sample of n=1200 in a=60 clusters is selected from a large population with S^2=500. In a published report, v(y ̅)=9 is reported. A colleague says there is no error in the calculation of the variance of the mean. Do you agree? Show a numeric justification for your answer. (Hint: What is the value of roh implied by this reported variance?)