Question

34. The table to the right shows the results of a survey in which 400 adults from the​ East, 400 adults from the​ South, 400 adults from the​ Midwest, and 400 adults from the West were asked if traffic congestion is a serious problem. Complete parts​ all parts.

Region	Percentage
East	34%
South	32%
Midwest	26%
West	57%

​Construct a​ 99% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem.

The​ 99% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem is left ___,___ (Round to three decimal places as​ needed.)

​Construct a​ 99% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem. Is it possible that these two proportions are​ equal? Explain your reasoning.

The​ 99% confidence interval for the proportion of adults from the South say traffic congestion is a serious problem is left ___,___. (Round to three decimal places as​ needed.)

Is it possible that these two proportions are​ equal?

Answer 1

a)

99% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem is left

p +- z(a/2)*sqrt(p*(1-p)/n)

z(a/2)= 2.576

p= 0.26

lower =0.26-2.576*SQRT(0.26*(1-0.26)/400) = 0.204

upper =0.26+2.576*SQRT(0.26*(1-0.26)/400) = 0.316

b)

99% confidence interval for the proportion of adults from the South say traffic congestion is a serious problem is left

p +- z(a/2)*sqrt(p*(1-p)/n)

z(a/2)= 2.576

p= 0.32

lower =00.32-2.576*SQRT(00.32*(1-00.32)/400)= 0.260

upper =00.32+2.576*SQRT(00.32*(1-00.32)/400)= 0.380

c)

yes, there are many values like (.204, 0.316) which fall in both CI

Hence, I can say that it possible that these two proportions are​ equal