document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=401195>Question 401195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A light-bulb manufacturer claims that the light bulbs produced by his company have an average life of 1200 hours. A consumer agency wishes to test this claim, against the alternative of fraudulent (i.e. the alternative that average life span is less than 1200 hours). A random sample of 16 bulbs is chosen from production and tested as the life times. The summary statistics turn out to  X=1148.5 hours and S^2=12544.224. Based on these summary statistics, and at the &#945;=0.05 level of significance\r<BR>\n" );
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document.write( "a) Obtain a 100(1-&#945; )% confidence interval for the population mean ( &#956; ).<BR>\n" );
document.write( "b) Formulate the corresponding hypothesis and test it. \r<BR>\n" );
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document.write( "How do I do This?<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 #283916 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=283916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  A light-bulb manufacturer claims that the light bulbs produced by his company have an average life of 1200 hours. A consumer agency wishes to test this claim, against the alternative of fraudulent (i.e. the alternative that average life span is less than 1200 hours). <BR>\n" );
document.write( "A random sample of 16 bulbs is chosen from production and tested as the life times. The summary statistics turn out to X=1148.5 hours and S^2=12544.224. Based on these summary statistics, and at the &#945;=0.05 level of significance \r<BR>\n" );
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document.write( "a) Obtain a 100(1-&#945; )% confidence interval for the population mean ( &#956; ).<BR>\n" );
document.write( "x-bar = 1148.5<BR>\n" );
document.write( "ME = 1.753*112/sqrt(16) = 49.08<BR>\n" );
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document.write( "95%CI: 1148.5-49.08 < u < 1148.5+49.08<BR>\n" );
document.write( "95%CI: 1099.42 < u < 1197.58<BR>\n" );
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document.write( "b) Formulate the corresponding hypothesis and test it. <BR>\n" );
document.write( "Ho: u = 1200<BR>\n" );
document.write( "Ha: u < 1200<BR>\n" );
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document.write( "ts = 1148.5<BR>\n" );
document.write( "t(1148.5) = (1148.5-1200)/[112/sqrt(16)] = -1.839<BR>\n" );
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document.write( "p-value = P(t< -1.839 when df= 15) = 0.0429<BR>\n" );
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document.write( "Conclusion: Since the p-value is < 5%, fail to reject Ho.<BR>\n" );
document.write( "The test supports Ho at the 5% level of significance.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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