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)

East 36% South 31% Midwest 27% West 54%

(a) Construct a​ 95% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem. The​ 95% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem is ​( _ , _ ) ​(Round to three decimal places as​ needed.)

Answer 1

Here, phat = 0.36 , n =400

The z value at 95% confidence interval is,

alpha = 1 - 0.95 = 0.05
alpha/2 = 0.05/2 = 0.025
Zalpha/2 = Z0.025 = 1.96

Margin of error = E =z *sqrt(phat*(1-phat)/n)
= 1.96 *sqrt(0.36 *(1-0.36)/400)
= 0.0470

The 95% confidence interval is

phat -E < p < phat +E

0.36 - 0.0470 < p < 0.36 + 0.0470

0.313 < p < 0.407

The​ 95% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem is ( 0.313 , 0.407)