document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1132704>Question 1132704</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A genetic experiment with peas resulted in one sample of offspring that consisted of 420 green peas and 159 yellow peas.<BR>\n" );
document.write( "a. Construct a 90​% confidence interval to estimate of the percentage of yellow peas.<BR>\n" );
document.write( "b. It was expected that​ 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not​ 25%, do the results contradict​ expectations?<BR>\n" );
document.write( "a. Construct a 90​% confidence interval. Express the percentages in decimal form.\r<BR>\n" );
document.write( "\n" );
document.write( "_ <p <_<BR>\n" );
document.write( "nothing ​(Round to three decimal places as​ needed.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #749828 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=749828\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) sample proportion of yellow peas = 159/(420+159) = 0.275<BR>\n" );
document.write( ":<BR>\n" );
document.write( "standard error = square root(0.275*(1=0.275)/(420+159)) = 0.019<BR>\n" );
document.write( ":<BR>\n" );
document.write( "alpha(a) = 1 -(90/100) = 0.10<BR>\n" );
document.write( ":<BR>\n" );
document.write( "critical probability(p*) = 1 -(a/2) = 0.95<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I assume the population is normally distributed and since the sample is > 30, a normal distribution is used to construct the 90% confidence interval<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The z-score associated with p* is 1.645, which is the critical value(CV)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Margin of error = CV * SE = 1.645 * 0.019 = 0.031<BR>\n" );
document.write( ":<BR>\n" );
document.write( "90% confidence interval is 0.275 + or - 0.031, (0.244, 0.306)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b)  The 90% confidence level means that we would expect 90% of the confidence interval estimates to include the population proportion for yellow peas.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Ho: X = 0.25<BR>\n" );
document.write( ":<BR>\n" );
document.write( "H1: X not = 0.25<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Ho is our null hypothesis and H1 implies a two-tailed test<BR>\n" );
document.write( ":<BR>\n" );
document.write( "z = (0.275-0.25)/0.019 = 1.316<BR>\n" );
document.write( ":<BR>\n" );
document.write( "since this is a two-tailed test, we reject Ho if 1.316 > 1.96 or if 1.316 < -1.96, since 1.316 < 1.96 we do not reject Ho<BR>\n" );
document.write( ":  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );