Repeat Exercise 16, for estimating the percentage of children who had previously had measles.
The file measles.dat contains data consistent with that obtained in a survey of parents whose children had not been immunized for measles during a recent campaign to immunize all children between the ages of 11 and 15. During the campaign, 7633 children from the 46 schools in the area were immunized; 9962 children whose records showed no previous immunization were not immunized. In a follow-up survey to explore why the children had not been immunized during the campaign, Roberts et al. (1995) sent questionnaires to the parents of a cluster sample of the 9962 children. Ten schools were randomly selected, then a sample of the Mi nonimmunized children from each school was selected and the parents of those children were sent a questionnaire. Not all parents responded to the questionnaire; you will examine the effects of non response in Exercise 13 of Chapter 8.
a. Estimate, separately for each school, the percentage of parents who returned a consent form (variable returnf ). For this exercise, treat the €œno answer€ responses (value 9) as not returned.
b. Using the number of respondents in school i as mi, construct the sampling weight for each observation.
c. Estimate the overall percentage of parents who received a consent form along with a 95% CI.
d. How do your estimate and interval in part (c) compare with the results you would have obtained if you had ignored the clustering and analyzed the data as an SRS? Find the ratio:

What is the effect of clustering?

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estimated variance from (c) estimated variance if the data were analyzed as an SRS