document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999082>Question 999082</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A manufacturer claims that at least 95% of the equipment that she supplied to a<BR>\n" );
document.write( "factory confirmed to the specification. An examination of a sample of 200 pieces<BR>\n" );
document.write( "of equipment revealed 18 were faulty. Test for her claim at levels of significance (a)<BR>\n" );
document.write( "0.01 and (b) 0.05<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616772 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=616772\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A manufacturer claims that at least 95% of the equipment that she supplied to a<BR>\n" );
document.write( "factory conformed to the specification. An examination of a sample of 200 pieces<BR>\n" );
document.write( "of equipment revealed 18 were faulty. Test for her claim at levels of significance <BR>\n" );
document.write( "(a) 0.01<BR>\n" );
document.write( "Ho: p >= 0.95 (claim)<BR>\n" );
document.write( "Ha: p < 0.95<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "p-hat = 182/200 = 0.91<BR>\n" );
document.write( "z(0.41) = (0.91-0.95)/sqrt[0.95*0.05/200] = -0.04/sqrt[0.95*0.05/200] <BR>\n" );
document.write( "= -2.5955<BR>\n" );
document.write( "--------------<BR>\n" );
document.write( "p-value = P(z < -2.5955) = 0.0047<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Conclusion: Since the p-value is less than 1%, reject Ho ; reject the claim.<BR>\n" );
document.write( " <BR>\n" );
document.write( "(b) 0.05<BR>\n" );
document.write( "Conclusion:: Since the p-value is less than 5%, reject Ho ; reject the claim.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );