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 32%; row 3, Midwest 27%; row 4, West 54%.EastSouthMidwestWest35%32%27%54%

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

WestWest

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

WestWest

who say traffic congestion is a serious problem is

​(nothing​,nothing​).

​(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

Given Data

n = 400

Probability :

East 35% = 0.35

South 32% = 0.32

Midwest 27% = 0.27

West 54% = 0.54

a) 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem:

p = P west = 0.54

q = 1- p = 1- 0.54 = 0.46

SE =

SE = 0.0249

95% CI =

% = 0.05

95% CI =  0.54 1.96* 0.0249

= 0.54 0.049

95% CI  = 0.491, 0.589

The​ 95% confidence interval for the proportion of adults from the West

who say traffic congestion is a serious problem is 0.491 to 0.589

​b)

95% confidence interval for the proportion of adults from the south who say traffic congestion is a serious problem:

p = P south = 0.32

q = 1- p = 1- 0.32 = 0.68

SE =

SE = 0.0233

95% CI =

% = 0.05

95% CI =  0.54 1.96* 0.0233

= 0.54 0.046

95% CI  = 0.494, 0.586

The​ 95% confidence interval for the proportion of adults from the south

who say traffic congestion is a serious problem is 0.494 to 0.586