The table shows the result of a survey in which separate samples of 400 adults e

Question

The table shows the result 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) Construct a 95 percentage confidence interval for the proportion of adults from the East who say traffic congestion is a serious problem. The 95 percentage 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.) Construct a 95 percentage confidence interval for the proportion of adults from West who say traffic congestion is a serious problem. The 95 percentage confidence interval for the proportion of adults from West who say traffic congestion is a serious problem is (Round to three decimal places as needed.)

Explanation / Answer

Q1.
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
Sample Size(n)=400
Sample proportion = x/n =0.34
Confidence Interval = [ 0.34 ±Z a/2 ( Sqrt ( 0.34*0.66) /400)]
= [ 0.34 - 1.96* Sqrt(0.001) , 0.34 + 1.96* Sqrt(0.001) ]
= [ 0.294,0.386]
Q2.
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
Sample Size(n)=400
Sample proportion = x/n =0.55
Confidence Interval = [ 0.55 ±Z a/2 ( Sqrt ( 0.55*0.45) /400)]
= [ 0.55 - 1.96* Sqrt(0.001) , 0.55 + 1.96* Sqrt(0.001) ]
= [ 0.501,0.599]

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