Homework Sourse400 adults from the East400 Adults who say that traffic cong
400 adults from the East,400
Adults who say that traffic congestion is a serious problem
EastEast
36%
SouthSouth
33%
MidwestMidwest
25%
WestWest
56%
(a) Construct a 99% confidence interval for the proportion of adults from the MidwestMidwest
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_ and _
(Round to three decimal places as needed.)
| 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 400adults 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 | |
| EastEast | 36% | |
| SouthSouth | 33% | |
| MidwestMidwest | 25% | |
| WestWest | 56% |
Solution
Confidence Interval For Proportion
CI = p ± Z a/2 Sqrt(p*(1-p)/n)))
x = Mean
n = Sample Size
a = 1 - (Confidence Level/100)
Za/2 = Z-table value
CI = Confidence Interval
Mean(x)=100
Sample Size(n)=400
Sample proportion = x/n =0.25
Confidence Interval = [ 0.25 ±Z a/2 ( Sqrt ( 0.25*0.75) /400)]
= [ 0.25 - 2.58* Sqrt(0) , 0.25 + 2.58* Sqrt(0) ]
= [ 0.194,0.306]
