document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1074706>Question 1074706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 747 hours. A random sample of 29 light bulbs has a mean life of 737 hours. Assume the population is normally distributed and the population standard deviation is 56 hours. At alpha&#945;equals=0.050&#8203;, do you have enough evidence to reject the&#8203; manufacturer's claim?  Identify the critical&#8203; value(s). Use technology.<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 #689662 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=689662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the claim is that the mean life of the bulb is at least 747 hours.\r<BR>\n" );
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document.write( "the sample of size 29 has a standard deviation of 56 and a mean life of 737 hours.\r<BR>\n" );
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document.write( "you would think that, if the mean life of the bulb is claiamed to be at least 747 hours, that it would be unusual for the mean life of a sample of 29 bulbs to be less than that.\r<BR>\n" );
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document.write( "the critical value for it being unusual is that less than 5% of multiple samples of 29 bulbs should have a mean life less than 747 hours.\r<BR>\n" );
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document.write( "what this says is that this particular sample should be unusual since it does have a mean life less than 747 hours.\r<BR>\n" );
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document.write( "the critical z-score with an alpha of .05 on the low end is equal to -1.65.\r<BR>\n" );
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document.write( "the z-score of the sample is calculated as follows:\r<BR>\n" );
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document.write( "z = (x-m)/s\r<BR>\n" );
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document.write( "x = 737<BR>\n" );
document.write( "m = 747<BR>\n" );
document.write( "s = sd / sqrt(n) = 56/sqrt(29) = 10.4\r<BR>\n" );
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document.write( "you get z = -10/10.4 = -.96\r<BR>\n" );
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document.write( "since the z-score of the sample is less than the critical z-score, than you can conclude that the fact that the mean of this sample is less than the assumed mean of the population is not unusual.\r<BR>\n" );
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document.write( "this means that you can expect it to occur in more than 5% of the samples of size 29 taken.\r<BR>\n" );
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document.write( "this would cause you to reject the claim that the mean life of this type of bulb is at least 747 hours.\r<BR>\n" );
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document.write( "that's my opinion based on the expectation that the mean life of the bulb is at least 747 hours.\r<BR>\n" );
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