You are interested in estimating the proportion of BHS students that want to return to in-person learning. You take an SRS of 110 BHS students, and 70 say they’d like to come back. Calculate a 97% confidence interval, using our 4-step process.

both equations and proportions are better.

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584