document.write( "Question 1095615: I am having trouble getting to the point of a final answer. I am able to solve the Margin of Error easy enough I cannot get to the 90% confidence interval.\r
\n" ); document.write( "\n" ); document.write( "Here is the problem: In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 355 accurate orders and 76 that were not accurate.\r
\n" ); document.write( "\n" ); document.write( "Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate?\r
\n" ); document.write( "\n" ); document.write( "What I have so far is CI 90% Za is 1.64 My MoE is 0.036 I cannot get to the
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\n" ); document.write( "\n" ); document.write( "Any help would be appreciated. Thank you \n" ); document.write( "
Algebra.Com's Answer #710113 by rothauserc(4718)\"\" \"About 
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The sample size is 355 + 76 = 431
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\n" ); document.write( "The sample proportion is 76 / 431 = 0.1763 approximately 0.18
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\n" ); document.write( "Standard Error(SE) = sqrt[ p * ( 1 - p ) / n ] = sqrt[0.18*(1-0.18)/431] = 0.0185
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\n" ); document.write( "alpha(a) = 1 - (90/100) = 0.10
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\n" ); document.write( "critical probability(p*) = 1 - α/2 = 0.95
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\n" ); document.write( "We express the critical value(CV) as a z score(sample size > 30, we can use the normal distribution), find the z-score having a cumulative probability equal to our p* value of 0.95. The associated CV is 1.645
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\n" ); document.write( "ME = CV * SE = 1.645 * 0.0185 = 0.0304 approximately 0.03
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\n" ); document.write( "90% confidence interval = 0.18 + or - 0.03 which is (0.15, 0.21)
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