document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204140>Question 1204140</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 95 with 31.6% successes. Enter your answer as a tri-linear inequality using decimals (not percents) accurate to three decimal places.\r<BR>\n" );
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document.write( " < p < \r<BR>\n" );
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document.write( "Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places. </SPAN>\n" );
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document.write( "phat = sample proportion = 0.316<BR>\n" );
document.write( "phat's job is to estimate the population proportion p\r<BR>\n" );
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document.write( "n = sample size = 95\r<BR>\n" );
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document.write( "At 90% confidence, the z critical value is approximately z = 1.645<BR>\n" );
document.write( "This is something to memorize.<BR>\n" );
document.write( "Alternatively you can use a Z table or stats calculator (such as a TI83).\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "E = margin of error for a proportion<BR>\n" );
document.write( "E = z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "E = 1.645*sqrt(0.316*(1-0.316)/95)<BR>\n" );
document.write( "E = 0.07846494809787<BR>\n" );
document.write( "E = 0.078465 approximately\r<BR>\n" );
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document.write( "Afterward we compute the lower and upper bounds (L and U)<BR>\n" );
document.write( "L = lower boundary<BR>\n" );
document.write( "L = phat - E<BR>\n" );
document.write( "L = 0.316 - 0.078465<BR>\n" );
document.write( "L = 0.237535<BR>\n" );
document.write( "L = 0.238\r<BR>\n" );
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document.write( "U = upper boundary<BR>\n" );
document.write( "U = phat + E<BR>\n" );
document.write( "U = 0.316 + 0.078465<BR>\n" );
document.write( "U = 0.394465<BR>\n" );
document.write( "U = 0.394\r<BR>\n" );
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document.write( "The 90% confidence interval in the format L < p < U would be <font color=red size=4>approximately 0.238 < p < 0.394</font><BR>\n" );
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