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 32%

Midwest 28%

West 55%

​(a) Construct a​ 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 is (___,___). ​(Round to three decimal places as​ needed.)

Answer 1

Solution: ​(a) Construct a​ 95% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem.

Answer: We are given

Proportion from Midwest 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 is given below:

Where is the critical value at 0.05 significance level and we can use standard normal table to its value.

Therefore, we have:

or [23.6%, 32.4%]

Therefore the 95% confidence interval for the proportion of adults from the Midwest who say traffic congestion is a serious problem is (0.236,0.324) or (23.6%, 32.4%)