document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193687>Question 1193687</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A genetic experiment involving peas yielded one sample of offspring consisting of 440 green peas and 154 yellow peas. Use<BR>\n" );
document.write( "a 0.05 significance level to test the claim that under the same circumstances, 23% of offspring peas will be yellow. Identify the<BR>\n" );
document.write( "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<BR>\n" );
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document.write( "What are the null and alternative hypotheses?\r<BR>\n" );
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document.write( "What is the test statistic?\r<BR>\n" );
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document.write( "What is the P value?\r<BR>\n" );
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document.write( "What is the conclusion about the null hypothesis? <BR>\n" );
document.write( "A:Reject the hypothesis because the P-value is less than or equal to the significance level, a .<BR>\n" );
document.write( "B: Fail to reject the null hypothesis because the P-value is greater than the significance level, a <BR>\n" );
document.write( "C:Fail to reject the null hypothesis because the P-value is less than or equal to the significance level, a . D:Reject the null hypothesis because the P-value is greater than the significance level, a \r<BR>\n" );
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document.write( "What is the final conclusion? <BR>\n" );
document.write( "A:There is not sufficient evidence to warrant rejection of the claim that 23% of offspring peas will be yellow<BR>\n" );
document.write( " B: There is sufficient evidence to warrant rejection of the claim that 23% of offspring peas will be yellow C: There is sufficient evidence to support the claim that less than 23% of offspring peas will be yellow D:There is not sufficient evidence to support the claim that less than 23% of offspring peas will be yellow </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825716 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825716\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: <=23% of peas are <BR>\n" );
document.write( "Ha: >23% of peas are yellow<BR>\n" );
document.write( "alpha=0.05 for this one way test prob {reject Ho|Ho true}<BR>\n" );
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document.write( "normal approximation has mean np=136.62<BR>\n" );
document.write( "variance is np(1-p)=105.20<BR>\n" );
document.write( "sd is sqrt (V)=10.26<BR>\n" );
document.write( "found 154<BR>\n" );
document.write( "so z=(153.5-136.62)/10.256 using the continuity correction factor.<BR>\n" );
document.write( "=1.645<BR>\n" );
document.write( "probability z is >1.645 is 0.050. This is a one way test, so will be half the p-value of a two way. \r<BR>\n" );
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document.write( "The answers to the multiple choice questions are A and B. One rejects Ho and concludes that there is sufficient evidence to warrant the claim that 23% of the peas are not yellow. \r<BR>\n" );
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document.write( "The way I would do this is with a one-sample two way proportion test<BR>\n" );
document.write( "Ho: p=0.23<BR>\n" );
document.write( "Ha: P NE 0.23<BR>\n" );
document.write( "alpha-0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "test statistic is a z=(p hat-p)/sqrt(0.23*0.77/594)<BR>\n" );
document.write( "critical value is |z|>1.96<BR>\n" );
document.write( "p hat=0.02593<BR>\n" );
document.write( "z= 0.0293/0.0173=1.693<BR>\n" );
document.write( "fail to reject Ho, p-value is 0.090. Two-way tests double the p-value of one way, since both sides have areas in the rejection region.  This is more exact.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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