document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204252>Question 1204252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two extrusion machines that manufacture steel rods are being compared. In a sample<BR>\n" );
document.write( "of 1000 rods taken from machine 1, 960 met specifications regarding length and<BR>\n" );
document.write( "diameter. In a sample of 600 rods taken from machine 2, 582 met the specifications.<BR>\n" );
document.write( "Are the two machines equally effective at producing rods that meet the specifications?<BR>\n" );
document.write( "Conduct a hypothesis test at 0.01 significance level to reach a conclusion. Use the Pvalue method </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #840402 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=840402\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p1 = 960/1000 = .96<BR>\n" );
document.write( "p2 = 582/600 = .97<BR>\n" );
document.write( "average of p1 + p2 = (960 + 582) / (1000 + 600) = .96375<BR>\n" );
document.write( "call that p0.<BR>\n" );
document.write( "standard error = sqrt((p0 * (1-p0) * (1/1000 + 1/600)) = .009652<BR>\n" );
document.write( "z-score = (.96 - .97) / .009652 = -1.036055<BR>\n" );
document.write( "area to the left of that = .150088<BR>\n" );
document.write( "that's the test p-value on the left of the confidence interval.<BR>\n" );
document.write( "same area ia on the right for a total test p-value of .300176.<BR>\n" );
document.write( "critical p-value is .01.<BR>\n" );
document.write( "since the test p-value is greater than the critical p-value, the results are not significant.<BR>\n" );
document.write( "the conclusion is that there is not enough evidence to show that the two samples are not equally effectivfe at meeting the specifications.<BR>\n" );
document.write( "this means that they can be considered to be equally effective at producing rods that meet the specifications.<BR>\n" );
document.write( "online calculator gives the same results plus or minus a few because of rounding, as shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/101501.jpg\">\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://sixsigmastudyguide.com/two-sample-test-of-proportions/#:~:text=Two%20sample%20Z%20test%20of%20proportions%20is%20the%20test%20to,that%20have%20some%20single%20characteristic.\" target = \"_blank\">https://sixsigmastudyguide.com/two-sample-test-of-proportions/#:~:text=Two%20sample%20Z%20test%20of%20proportions%20is%20the%20test%20to,that%20have%20some%20single%20characteristic.</a> </SPAN>\n" );
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