Question

The table shows the results of a survey in which separate samples of 400 adults each form the East, South, Midwest, and West were asked if traffic congestion is a serious problem in their community

East-36% South-32% Midwest-28% West-57%

The 95% confidence interval for the proportion of adults from the South 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____,____?

The 95% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem____,____?

The 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem____,____?

Answer 1

z value at 95% = 1.96

n = 400

p = 0.32

CI = p +/- z *sqrt(p *(1-p)/n)
= 0.32 +/- 1.96 *sqrt(0.32*(1-0.32)/400)
= (0.2743,0.3657)
The 95% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem_(0.2743,0.3657

when p = 0.36

CI = p +/- z *sqrt(p *(1-p)/n)
= 0.36 +/- 1.96 *sqrt(0.36*(1-0.36)/400)
= (0.3130 , 0.4070)

The 95% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem (0.3130 , 0.4070)

when p = 0.28

CI = p +/- z *sqrt(p *(1-p)/n)
= 0.28 +/- 1.96 *sqrt(0.28*(1-0.28)/400)
= (0.2360 , 0.3240)

The 95% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem (0.2360 , 0.3240)

When p = 0.57

CI = p +/- z *sqrt(p *(1-p)/n)
= 0.57 +/- 1.96 *sqrt(0.57*(1-0.57)/400)
= (0.5215 , 0.6185)

The 95% confidence interval for the proportion of adults from the West who say traffic congestion is a serious problem(0.5215 , 0.6185)