Question

please answer this question

A polling firm surveyed 1000 adults from one country about r form of the country's senate. Of these, 26% of people in City A supported abolishing the senate, compared with 51% in City B Construct a 95% confidence l eral forthe difference in support between City A and City B Assume that 35.9% of the adults survey ere i City A and 21.1% ere in City B ) Let adults C y A be populatio Select the correct choice below and, if necessary, fill in the answer boxes within your choice. ⓔA. The 95% confidence interval is between.%and»%. O B. The interval should not be calculated because the assumptions and conditions are not met and cannot be reasonably assumed to be met 1 and adults m C B bepopula on 2. (Round to one decimal place as needed. Use ascending order.)

Answer 1

p1^ = 0.26 , p2^ = 0.49

n = 1000

confidence interval

=(p1^ - p2^) $\pm$  z s.e

p1^ - p2^ = 0.26 -0.49 = -0.23

n1 = 35.9 % *1000 = 359 , n2 = 274

s.e = sqrt(p1*q1 /n1 + p2*q2/n2)

= sqrt(0.26*0.74 /359 + 0.49*0.51/274) =0.03805

z = 1.96 for 95 % confidence level

hence interval is

(-0.23 - 1.96*0.03805 , -0.23 + 1.96 *0.03805)

=( -0.30457 , -0.155422 )