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.

Adults who say that traffic
Congestion is a problem
East 36%
South 31%
Midwest 27%
West 57%

Complete parts​ (a) and​ (b).

(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 East who say traffic congestion is a serious problem is (__),(__)

(Round to three decimal places as​ needed.)

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

The​ 99% confidence interval for the proportion of adults from the South who say traffic congestion is a serious problem is (__), (__)

(Round to three decimal places as​ needed.)

Answer 1

The statistical software output for this problem is:

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:

Proportion	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
p	108	400	0.27	0.022197973	0.22649277	0.31350723

One sample proportion summary confidence interval:
p : Proportion of successes
Method: Standard-Wald

99% confidence interval results:

Proportion	Count	Total	Sample Prop.	Std. Err.	L. Limit	U. Limit
p	124	400	0.31	0.023124662	0.25043482	0.36956518

Hence,

a) 95% confidence interval for midwest:

(0.226, 0.314)

b) 99% confidence interval for south:

(0.250, 0.370)