document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205308>Question 1205308</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A factory manufactures light bulbs for distribution under 2 different brands. Brand A bulbs have an<BR>\n" );
document.write( "average life of 1800 hours with a standard deviation of 240 hours; Those of mark B have an average life<BR>\n" );
document.write( "of 1450 hours with a standard deviation of 150 hours. A sample of 250 light bulbs is taken from each<BR>\n" );
document.write( "brand. Describe completely this situation, define all the data, and explain the method and all steps of<BR>\n" );
document.write( "computation. How likely is the average lifespan of Brand A bulbs to be at least 400 hours longer than<BR>\n" );
document.write( "that of Brand B bulbs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842073 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=842073\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is my best shot at what i think is the way to analyze this.<BR>\n" );
document.write( "i'm using a two sample z-test.<BR>\n" );
document.write( "referenceto that can be found at <a  rel=nofollow HREF= \"\" target = \"_blank\"></a>\r<BR>\n" );
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document.write( "brand A has a mean of 1800 with a standard deviation of 240.<BR>\n" );
document.write( "brand B has a mean of 2450 with a standard deviation of 150.<BR>\n" );
document.write( "a sample of size 250 is taken from the population of both brands.\r<BR>\n" );
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document.write( "the mean of brand A is compared to the mean of brand B using a two sample z-test.<BR>\n" );
document.write( "z-score formula is z = (x-m)/s<BR>\n" );
document.write( "z is he z-score.<BR>\n" );
document.write( "x is the mean of brand A.<BR>\n" );
document.write( "m is the mean of brand B.<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "s = sqrt(d1^2/n1 + d2^2/n2)<BR>\n" );
document.write( "d1 is the standard deviation of brand A.<BR>\n" );
document.write( "d2 is the standard deviation of brand B.<BR>\n" );
document.write( "n1 and n2 are the sample size of brand A and brand B.<BR>\n" );
document.write( "this is the same at 250.<BR>\n" );
document.write( "formula becomes s = sqrt(240^2/250 + 150^2/250) = 17.89972.\r<BR>\n" );
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document.write( "z-score formula becomes z = (1800 - 1450) / 17.89972 = 19.55613.<BR>\n" );
document.write( "this is a very high z-score, indicating that the mean of brand A is clearly greater than the mean of brand B and that the probability of getting a difference greater than 350 is effectively 0.\r<BR>\n" );
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document.write( "based on that, then the probability of getting a mean for brand A that is more than 400 hours greater than the mean for brand B is even less probable, meaning that it is also effectively 0.\r<BR>\n" );
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document.write( "here are the results of the two sample t-test using the calculator at <a  rel=nofollow HREF= \"https://www.statskingdom.com/120MeanNormal2.html\" target = \"_blank\">https://www.statskingdom.com/120MeanNormal2.html</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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