document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210248>Question 1210248</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey was given to a random sample of 105 voters in the United States to ask about their preference for a presidential candidate. Of those surveyed, 84 respondents said that they preferred Candidate A. At the 95% confidence level, what is the margin of error for this survey expressed as a proportion to the nearest thousandth? </SPAN>\n" );
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document.write( "n = 105 = sample size<BR>\n" );
document.write( "x = 84 = number of people who prefer candidate A<BR>\n" );
document.write( "phat = x/n = 84/105 = 0.8 = sample proportion of those who prefer candidate A<BR>\n" );
document.write( "The job of phat is to estimate the population proportion p.<BR>\n" );
document.write( "The name \"phat\" is due to a hat over top the letter p. \r<BR>\n" );
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document.write( "At 95% confidence, the z critical value is approximately z = 1.96<BR>\n" );
document.write( "This value is used very frequently in statistics that I recommend you memorize it.<BR>\n" );
document.write( "Alternatively you can have it on a reference sheet or look it up online.\r<BR>\n" );
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document.write( "So we have these key values:<BR>\n" );
document.write( "z = 1.96 (approx)<BR>\n" );
document.write( "phat = 0.8<BR>\n" );
document.write( "n = 105\r<BR>\n" );
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document.write( "Those values lead to:<BR>\n" );
document.write( "E = margin of error for the sample proportion<BR>\n" );
document.write( "E = z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "E = 1.96*sqrt(0.8*(1-0.8)/105)<BR>\n" );
document.write( "E = 0.076510565719 approximately<BR>\n" );
document.write( "E = 0.077 when rounding to the nearest thousandth, i.e. 3 decimal places.\r<BR>\n" );
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document.write( "Answer: <font color=red>0.077</font><BR>\n" );
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