document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1141673>Question 1141673</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the P-value for the indicated hypothesis test.\r<BR>\n" );
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document.write( "A manufacturer claims that fewer than 8% of its products are defective. In a random sample of 120 such products, 12% are defective. Find the P-value for a test to support the manufacturer's claim. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #762329 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=762329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given the assumptions of normality and randomness are present,<BR>\n" );
document.write( "a one way test (fewer than 8% is one way) is a one sample proportion test with critical value z<-1.645. Note, 12% is not an integer, so one can use 14/120 as the nearest integer to 12% and 10/120 for the nearest integer to 8%. This is an important distinction in this kind of problem where exact per cents do not occur for specific numbers of people.<BR>\n" );
document.write( "Here, it is done using per cents\r<BR>\n" );
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document.write( "z=(.08-.12)/sqrt(p*(1-p)/n)<BR>\n" );
document.write( "=-0.04/sqrt (.08*.92/120)<BR>\n" );
document.write( "=-0.04/0.0248<BR>\n" );
document.write( "=-1.61<BR>\n" );
document.write( "p-value is 0.0537<BR>\n" );
document.write( "I suspect this is the value that is desired, but it is important to recognize that this is a discrete function here and not continuous.\r<BR>\n" );
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document.write( "Here, it is done using integers closest to the given per cents<BR>\n" );
document.write( "z=(10-14)/120/sqrt (10/120)(110/120)/120<BR>\n" );
document.write( "=-0.03333/0.0252<BR>\n" );
document.write( "=-1.32 p-value is 0.0934\r<BR>\n" );
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document.write( "And if one wishes for an exact result, the binomial formula may be used. </SPAN>\n" );
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