document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204904>Question 1204904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A genetic experiment involving peas yielded one sample of offspring consisting of 433 green peas and 166 yellow peas. Use a 0.01 significance level to test the claim that under the same​ circumstances, 26​% of offspring peas will be yellow. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842282 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=842282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size = 433 + 166 = 599<BR>\n" );
document.write( "green peas = 433<BR>\n" );
document.write( "yellow peas = 166\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "p = .2771285476<BR>\n" );
document.write( "q = 1-p = .7228714524\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "mean = p<BR>\n" );
document.write( "standard error = sqrt(p*q/n) = .018287644<BR>\n" );
document.write( "n = sample size\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (x-m)/s is the formula used.<BR>\n" );
document.write( "z is the critical z-score at 99% two tail confidence level.<BR>\n" );
document.write( "x is the test mean of .26<BR>\n" );
document.write( "m is the sample mean of p<BR>\n" );
document.write( "s is the standard error\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "critical z-score at 99% two tail confidence interval = plus or minus 2.5758 rounded to 4 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula to find the test z-score is z = (.26 - .2771285476) / .018287644 = -.9366186037.<BR>\n" );
document.write( "test z-score is less than critical z-score of -2.5758.<BR>\n" );
document.write( "this indicates that the test value of .26 is within the 99% confidence interval limits of the sample mean of p.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this indicates that the percentage of yellow peas equal to 26% under the same circumstances is reasonable to assume.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the test p-value was .1745 which was higher than the critical p-value of .005 on the low end of the confidence interval (.01 / 2 = .005 on the low end of the confidence interval and .005 on the high end of the confidence interval)>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "null hypothesis is that p = .26 is possible under the same circumstance.<BR>\n" );
document.write( "alternate hypothesis is that p = .26 isn't.<BR>\n" );
document.write( "test p-value = .1745<BR>\n" );
document.write( "this is greater than critical p-value of .005 on the low end of the confidence interval.<BR>\n" );
document.write( "conclusion is that p-value of .26 is entirely reasonable under the same conditions as it is well within the confidence interval.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to find the confidence interval limits, do the following.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the low end of the confidence interval, you get -2.5758 = (x - .2771285476) / .018287644.<BR>\n" );
document.write( "solve for x to get x = -2.5758 * .018187644 + .2771285476 = .2300232342.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "on the high end of the confidence interval, you get 2.5758 = (x - .2771285476) / .018287644.<BR>\n" );
document.write( "solve for x to get x = 2.5758 * .018187644 + .2771285476 = .324233861.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your 99% confidence interval is from .2300 to .3242 rounded to 4 decimal places.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( ".26 is well within those confidence interval limits.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );