SOLUTION: Good day please kindly help me with the following stats problem I will highly appreciate your method used I tried and my solutions is: .5479 and .5510 Questions A polling

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Question 1132155: Good day please kindly help me with the following stats problem I will highly appreciate your method used
I tried and my solutions is:
.5479 and .5510
Questions
A polling firm samples 600 likely voters and asks them whether they favour a proposal involving school bonds. A total of 330 of these voters indicate that they favour the proposal.Estimate the true population proportion of voters who do not favour the proposal with a 99% level of confidence.

Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
600 - 330 = 270
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sample proportion of voters who do not support proposal is 270/600 = 0.45
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standard error(SE) of the proportion = square root(0.45 * (1-0.45) / 600) = 0.0203
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margin of error(ME) = critical value(CV) * SE
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alpha(a) = 1 -(99/100) = 0.01
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critical probability(p*) = 1 -(a/2) = 0.995
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CV is expressed as a z-score with the associated p*, NOTE we use z-score since the sample size is > 30
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CV = 2.58
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ME = 2.58 * 0.0203 = 0.0524
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99% confidence interval is sample proportion + or - ME = 0.45 + or - 0.0524, (0.3976, 0.5024)
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