document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209020>Question 1209020</A>: <I><SPAN STYLE=\"word-break: break-all;\">  genetic experiment with peas resulted in one sample of offspring that consisted of 447 green peas and 158 yellow peas.<BR>\n" );
document.write( "a. Construct a 95% confidence interval to estimate of the percentage of yellow peas </SPAN>\n" );
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document.write( "x = number of yellow peas = 158<BR>\n" );
document.write( "n = sample size = 447 green + 158 yellow = 605 total.\r<BR>\n" );
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document.write( "phat = sample proportion of yellow peas<BR>\n" );
document.write( "phat = x/n <BR>\n" );
document.write( "phat = 158/605<BR>\n" );
document.write( "phat = 0.26115702 approximately<BR>\n" );
document.write( "Around 26.12% of the peas in the sample are yellow.\r<BR>\n" );
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document.write( "At 95% confidence, the z critical value is roughly z = 1.960<BR>\n" );
document.write( "This is a value to memorize since it comes up a lot in statistics. <BR>\n" );
document.write( "Or this value is something you would look up in a textbook, reference sheet, or website.\r<BR>\n" );
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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 = 1.960*sqrt(0.26115702*(1-0.26115702)/605)<BR>\n" );
document.write( "E = 0.03500300\r<BR>\n" );
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document.write( "L = lower boundary of the confidence interval<BR>\n" );
document.write( "L = phat - E<BR>\n" );
document.write( "L = 0.26115702 - 0.03500300<BR>\n" );
document.write( "L = 0.22615402<BR>\n" );
document.write( "L = 0.226\r<BR>\n" );
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document.write( "U = upper boundary of the confidence interval<BR>\n" );
document.write( "U = phat + E<BR>\n" );
document.write( "U = 0.26115702 + 0.03500300<BR>\n" );
document.write( "U = 0.29616002<BR>\n" );
document.write( "U = 0.296\r<BR>\n" );
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document.write( "The 95% confidence interval in the format L < p < U is approximately <font color=red>0.226 < p < 0.296</font>\r<BR>\n" );
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document.write( "This can be condensed to  <font color=red>(0.226, 0.296)</font>\r<BR>\n" );
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document.write( "It indicates we are 95% confident that the population proportion of yellow peas is somewhere between 22.6% and 29.6%<BR>\n" );
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