document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=294537>Question 294537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At &#945; = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population\r<BR>\n" );
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document.write( "Correct Answer Frequency<BR>\n" );
document.write( "A 8<BR>\n" );
document.write( "B 8<BR>\n" );
document.write( "C 9<BR>\n" );
document.write( "D 11<BR>\n" );
document.write( "E 14<BR>\n" );
document.write( "Total 50\r<BR>\n" );
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document.write( "Can you help me solve this problem. I am supposed to create a null and alternative hypothesis. Show how the degress of freedom are calculated, find the critical value of chi squared and interpret the p-value as well as check for small expected frequencies </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212422 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=212422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Prof. Green’s multiple-choice exam had 50 questions with the distribution of correct answers shown below. Research question: At &#945; = .05, can you reject the hypothesis that Green’s exam answers came from a uniform population <BR>\n" );
document.write( "Correct Answer Frequency<BR>\n" );
document.write( "A 8<BR>\n" );
document.write( "B 8<BR>\n" );
document.write( "C 9<BR>\n" );
document.write( "D 11<BR>\n" );
document.write( "E 14<BR>\n" );
document.write( "Total 50 <BR>\n" );
document.write( "Can you help me solve this problem. I am supposed to create a null and alternative hypothesis. Show how the degress of freedom are calculated, find the critical value of chi squared and interpret the p-value as well as check for small expected frequencies<BR>\n" );
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document.write( "The expected values are 10,10,10,10,10<BR>\n" );
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document.write( "Ho: all frequencies or propabilites are equal<BR>\n" );
document.write( "Ha: at least one of the probs is different<BR>\n" );
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document.write( "Determine the O-E differences for each category:<BR>\n" );
document.write( "-2,-2,-1,+1,+4<BR>\n" );
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document.write( "Calculate the Chi-Sq test statistic for <BR>\n" );
document.write( "the data based on Chi-Sq = sim[(O-E)^2/E] = (4+4+1+1+16)/10 = 2.6<BR>\n" );
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document.write( "degrees of freedom = 5-1 = 4<BR>\n" );
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document.write( "Critical value for df=4 and alpha = 5% = 9.488<BR>\n" );
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document.write( "p-value = P(Chi-Sq >2.6 when df=4) = Chi-Sqcdf(2.6,1000,4) = 0.6268<BR>\n" );
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document.write( "Conclusion: Since the p-value is greater than 5% fail to reject Ho.<BR>\n" );
document.write( "That is the same as saying the test stat is not in the reject interval.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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