document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193836>Question 1193836</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. Liwanag Bulb Company claims that it sells light bulbs with an average life of <BR>\n" );
document.write( "1000 hours. A sample of 64 new bulbs were allowed to burn out to test this claim. <BR>\n" );
document.write( "The average lifetime of the sample was found to be 975 hours with a standard <BR>\n" );
document.write( "deviation of 75 hours. Does this indicate that the average life of the bulb is not <BR>\n" );
document.write( "1000 hours? Use 5% level of significance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825918 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=825918\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since you are using the standard deviation of the sample, the use of the t-score is indicated.<BR>\n" );
document.write( "in this case, it probably doesn't make much difference.<BR>\n" );
document.write( "i'll show you why.<BR>\n" );
document.write( "standard error = 75 / sqrt(64) = 75/8 = 9.375<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the assumed population mean.<BR>\n" );
document.write( "s = standard error.<BR>\n" );
document.write( "the formula becomes:<BR>\n" );
document.write( "z-score = (975 - 1000) / 9.375 = -2.67<BR>\n" );
document.write( "t-score is the same.<BR>\n" );
document.write( "the probability that a z-score less than -2.67 will occur is equal to .00379.<BR>\n" );
document.write( "the probability that a t-score with 63 degrees of freedom is less than -2.67 is equal to .00482.<BR>\n" );
document.write( "a two tailed confidence interval of 95% has an area of .025 to the left of it and .025 to the right of it.<BR>\n" );
document.write( ".0038 and.0048 are both less than that, making the results significant whether or not you use the z-score or the t-score.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );