document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206985>Question 1206985</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two random samples are taken, one from among first-year students and the other from among fourth-year students at a public university. Both samples are asked if they favor modifying the student Honor Code. A summary of the sample sizes and number of each group answering <BR>\n" );
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document.write( "First-Years (Pop. 1):Fourth-Years (Pop. 2):n1=97,n2=91,x1=56x2=60<BR>\n" );
document.write( "Is there evidence, at an α=0.055<BR>\n" );
document.write( " level of significance, to conclude that there is a difference in proportions between first-years and fourth-years? Carry out an appropriate hypothesis test, filling in the information requested.\r<BR>\n" );
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document.write( "A. The value of the test statistic (rounded to 3 decimal places): <BR>\n" );
document.write( "Note: For the next part, your answer should use interval notation. An answer of the form (−∞,a)<BR>\n" );
document.write( " is expressed (-infty, a), an answer of the form (b,∞)<BR>\n" );
document.write( " is expressed (b, infty), and an answer of the form (−∞,a)∪(b,∞)<BR>\n" );
document.write( " is expressed (-infty, a)U(b, infty).\r<BR>\n" );
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document.write( "B. The rejection region for the standardized test statistic: <BR>\n" );
document.write( "C. The p-value is </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844763 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=844763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> using pooled standard error, i get z = -1.156.\r<BR>\n" );
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document.write( "using un-pooled standard error, i get z = -1.161.\r<BR>\n" );
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document.write( "the two-tailed alpha is equal to .055.<BR>\n" );
document.write( "that would be a tail of alpha/2 = .0275 on the left and a tail of alpha/2 = .0275 on the right.\r<BR>\n" );
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document.write( "at .055 two tailed alpha, the critical z-score is plus or minus 1.9189.\r<BR>\n" );
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document.write( "z-score of -1.156 and -1.161 are less than -1.9189, so the results are not significant regardless if you used pooled or un-pooled standard error.\r<BR>\n" );
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document.write( "answers to your questions:\r<BR>\n" );
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document.write( "A.  test statistic is z = -1.156 (pooled standard error is assumed).\r<BR>\n" );
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document.write( "B.  the rejection region for the test is z = (-infinity,-1.9189) union (1.9189,infinity).\r<BR>\n" );
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document.write( "C.  the p-value of the test is .2476.<BR>\n" );
document.write( "that's a two-tailed p-value, meaning half is on the left tail and half is on the right tail.\r<BR>\n" );
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document.write( "here's what the results look like on a z-score calculator.\r<BR>\n" );
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