Question

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​ (a) and​ (b). Adults who say that traffic congestion is a serious problem East 34​% South 33​% Midwest 27​% West 56​% ​(a) Construct a​ 99% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem. The​ 99% confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem is left parenthesis nothing comma nothing right parenthesis . ​(Round to three decimal places as​ needed.)

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 3
Alternative Hypothesis, Ha: μ ≠ 3

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (2.8 - 3)/(0.5/sqrt(75))
z = -3.46

P-value Approach
P-value = 0.0005
As P-value < 0.02, reject the null hypothesis.

2)

sample proportion, = 0.34
sample size, n = 400
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.34 * (1 - 0.34)/400) = 0.0237

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0237
ME = 0.0611

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.34 - 2.58 * 0.0237 , 0.34 + 2.58 * 0.0237)
CI = (0.279 , 0.401)