A researcher took an SRS of 4 high schools from a region with 29 high schools for a study on the prevalence of smoking among female high school students in the region.
The results were as follows:

a. Estimate the percentage of female high school students in the region who smoke, along with a 95% CI.
b. Estimate the total number of female high school students in the region who smoke, along with a 95% CI.
c. The researcher now wants to study the prevalence of smoking and other risk behaviors among female high school students in a different region with 35 high schools. She intends to drive to n of the schools and then interview some or all of the female students in the selected schools. Assuming that MSB and MSW are similar in the two regions, use information from the study of 4 schools to estimate R2a and design a cluster sample for the new study. Suppose it takes about 50 hours per school to contact school officials, obtain permission, obtain a list of female students, and travel back and forth. Although interviews themselves are only about 10 minutes, it takes about 30 minutes per interview obtained to allow for additional scheduling of no-shows, obtaining parental permission, and other administrative tasks. The investigator would like to spend 300 hours or less on the data collection.

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Number of Number of Femal Number of Female Number of SchoolStudents Students in Sco Students Interviewed Smokers 1471 890 1021 1587 792 447 511 800 25 15 20 40 10 3 4 27