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Institutional surveys are the surveys in which the primary sampling units are the institutions, for instance, hospitals. Within each of the sampled institution, a sample of the patient records is selected.
The basic purpose of the two-stage design (compared to the simple random sample) are to reduce the number of institutions which are required to be subsampled, and to ignore constructing a sampling frame of the patient records for the whole population. Stratified sampling including selecting institutions with the differing probabilities based on some institutional characteristic (like size) is typically used to reduce the variability of the estimators.
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How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;
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