SOLUTION: A random sample of 800 registered voters in Flagstaff found 456 registered voters who support immigration reform. Find a 95% confidence interval for the true percent of registered

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Question 1039097: A random sample of 800 registered voters in Flagstaff found 456 registered voters who support immigration reform. Find a 95% confidence interval for the true percent of registered voters in Flagstaff who support immigration reform. Express your results to the nearest hundredth of a percent. .
Answer:
____ to____%
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Given information
x = 456 (number of successes)
n = 800 (sample size)
Confidence Level = 95%
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What we want to find:
We want to find the lower (L) and upper (U) boundaries of the confidence interval
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The critical value of the 95% confidence interval is z = 1.96 (approximately). You can determine this by using a table like this one. Look at the confidence level 95% (bottom of page) then look directly above it to find the value of 1.960 which is the same as 1.96


Sample proportion
p = x/n = 456/800 = 0.57


Standard Error (SE)
SE+=+sqrt%28%28p%2A%281-p%29%29%2Fn%29
SE+=+sqrt%28%280.57%2A%281-0.57%29%29%2F800%29
SE+=+sqrt%28%280.57%2A%280.43%29%29%2F800%29
SE+=+sqrt%280.2451%2F800%29
SE+=+sqrt%280.000306375%29
SE+=+0.01750357106421


Margin of Error (ME)
ME+=+z%2ASE
ME+=+1.96%2A0.01750357106421
ME+=+0.03430699928586


The lower boundary of the confidence interval is
L+=+p+-+ME
L+=+0.57+-+0.03430699928586
L+=+0.53569300071414
That turns into 53.569300071414% which rounds to 53.57%

So L = 53.57% approximately


The upper boundary of the confidence interval is
U+=+p+%2B+ME
U+=+0.57+%2B+0.03430699928586
U+=+0.60430699928587
That turns into 60.430699928587% which rounds to 60.43%

So U = 60.43% approximately


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To recap, the lower and upper bound (L and U respectively) of the confidence interval is

L = 53.57%
U = 60.43%

where the boundaries are in percentage form

Final Answer:
   53.57    to    60.43   %