Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have cell phones. Three hundred randomly selected adult residents in this city are surveyed to determine whether they have cell phones. Of the 300 people sampled, 274 responded yes - they own cell phones. Using a 95% confidence level, compute a confidence interval estimate for the true proportion of adult residents of this city who have cell phones.

Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ∠dab = x, and ∠abc = 90◦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ∠pad = ∠pbc. but pab is isosceles, hence ∠pab = ∠pba. subtracting, gives x = ∠pad−∠pab = ∠pbc −∠pba = 90◦. this is a preposterous conclusion – just where is the mistake in the "proof" and why does the argument break down there?

Can some one me, i’ve been asking for so long

Either enter an exact answer in terms of \piπ or use 3.143.14 for \piπ and enter your answer as a decimal.