Question

The table shows the results of a survey in which separate samples of 400 adults each from the​ East, South,​ Midwest, and West were asked if traffic congestion is a serious problem in their community. Complete parts​ (a) and​ (b).

A table consists of four rows containing the following information from top to bottom, with row listed first and information listed second; row 1, East 35%; row 2, South 33%; row 3, Midwest 28%; row 4, West 57%.EastSouthMidwestWest35%33%28%57%

​(a) Construct a​ 95% confidence interval for the proportion of adults from the

MidwestMidwest

who say traffic congestion is a serious problem.The​ 95% confidence interval for the proportion of adults from the

MidwestMidwest

who say traffic congestion is a serious problem is

​(0.2360.236​,0.3240.324​).

​(Round to three decimal places as​ needed.)

​(b) Construct a​ 95% confidence interval for the proportion of adults from the

SouthSouth

who say traffic congestion is a serious problem. The​ 95% confidence interval for the proportion of adults from the

SouthSouth

who say traffic congestion is a serious problem is

​(nothing​,nothing​).

​(Round to three decimal places as​ needed.)

Answer 1

z value at 95% = 1.96

n = 400

a)

when p = 0.28

CI = p +/- z *sqrt(p *(1-p)/n)
= 0.28 +/- 1.96 *sqrt(0.28*(1-0.28)/400)
= (0.236 , 0.324)

The 95% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem (0.236 , 0.324)
b)
p = 0.33

CI = p +/- z *sqrt(p *(1-p)/n)
= 0.33 +/- 1.96 *sqrt(0.33*(1-0.33)/400)
= (0.284,0.376)

The 95% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem_(0.284,0.376)