document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200911>Question 1200911</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A supplier of USB flash claims that more than 11% of the USBs are defective. In a random sample of 167 USBs, it is found that 37 are defective, but the supplier claims that this is only a sample fluctuation. At the 0.05 level of significance, test the supplier's claim that  more than 11% are defective. \r<BR>\n" );
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document.write( "a. Is this  (a: one sample mean test, b: two sample mean test, c: one proprtion test, d: ch-square test)\r<BR>\n" );
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document.write( "b. Since the test statistic (round to 2 decimals): </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #836720 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=836720\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population p = .11<BR>\n" );
document.write( "population q = 1 - .11 = .89<BR>\n" );
document.write( "sample size is 167.<BR>\n" );
document.write( "37 are defective.<BR>\n" );
document.write( "sample p = 37/167 = .2215568862<BR>\n" );
document.write( "standard error of the test is equal to sqrt(population p * population q / 167) = sqrt(.11 * .89 / 167) = .0242121363.<BR>\n" );
document.write( "z-score = (.2215568862 - .11) / .0242121363 = 4.607478034<BR>\n" );
document.write( "area to the right of that = .000002040040862.<BR>\n" );
document.write( "that's significantly less than the critical p-value of .05.<BR>\n" );
document.write( "the probability  that the resuls is a fluctuation in smple means is pretty close to 0.<BR>\n" );
document.write( "the conclusion i that the preponderance of the evidence indicates that more than 11% of the USBs are defective, rejecting the claim that it's no more than 11%.\r<BR>\n" );
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document.write( "this is a one sample proportion test.<BR>\n" );
document.write( "the critical p-value is .05<BR>\n" );
document.write( "the test p-value is 0, rounded to two decimal places.\r<BR>\n" );
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document.write( "here are the results using the proportion calculator at <a  rel=nofollow HREF= \"https://www.statskingdom.com/111proportion_normal1.html\" target = \"_blank\">https://www.statskingdom.com/111proportion_normal1.html</a>\r<BR>\n" );
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document.write( "differences between the calculator numbers and the ones i calculated have an insignificant impact to the result and are more than likely due to rounding differences.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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