document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463276>Question 463276</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Historical data show that 4% of the components produced by a certain manufacturer are defective.Someone challenged the figure of 4% and the management wanted to test whether this claim has to be modified. If a random sample of 500 items resulted in 16 defective ones, is this significant evidence that the claim is incorrect?<BR>\n" );
document.write( "By considering a significance level alpha = 0.05, what is the lowest rate of defective components that the manufacturer can claim, with the same experimental test results?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317433 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=317433\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> H[o]:.04n=defective.<BR>\n" );
document.write( "H[a]:.04n<>defective.<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=p%5Bo%5D=.04 ALIGN=MIDDLE  ALT=\"mu=p%5Bo%5D=.04\"   DISABLED_style= \"max-width:90%; height:auto;\" >, q=.96<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sigma=sqrt%28pq%2Fn%29=sqrt%28.04%2A.96%2F500%29=.00876 ALIGN=MIDDLE  ALT=\"sigma=sqrt%28pq%2Fn%29=sqrt%28.04%2A.96%2F500%29=.00876\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=16%2F500=.032 ALIGN=MIDDLE  ALT=\"P=16%2F500=.032\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=%28P-p%5Bo%5D%29%2Fsigma=%28.032-.04%29%2F.00876=+-0.913%29 ALIGN=MIDDLE  ALT=\"z=%28P-p%5Bo%5D%29%2Fsigma=%28.032-.04%29%2F.00876=+-0.913%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since -0.913 is more than -1.96. This is not significant evidence that the claim is incorrect.<BR>\n" );
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document.write( "(x-.04)/.00876=-1.96<BR>\n" );
document.write( "x-.04=-.0172<BR>\n" );
document.write( "x=.0228  the lowest rate of defective components that the manufacturer can claim, with the same experimental test results.<BR>\n" );
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document.write( "Ed </SPAN>\n" );
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