:1. Solution. Since 240 is (240/400)x100 = 60% of the sample,
the center of the confidence interval is 60%. The upper endpoint
is two SE's above the center, since it is a 95% confidence
interval. We figure out the SE of the estimate by the
"bootstrap" method. We estimate the SD of the box (for the box
model) as the square root of .6x.4, or the square root of .24,
which is about .49. The SE of the total number of students in
the sample who wear glasses is .49 times the square root of 400,
or .49x20 = 9.80. The SE of the percentage of the students in
the sample who wear glasses is (9.8/400) x 100% = 9.8/4 = 2.45%.
The upper endpoint of the 95% confidence interval is 60 + (2 x
2.45) = 60 + 4.9 = 64.9%.