document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205768>Question 1205768</A>: <I><SPAN STYLE=\"word-break: break-all;\"> It is claimed that a random sample of 49 tyres has mean life of 15200 km. This sampled was drawn from a population whose mean is 15150 km's and a standard deviation of 1200 km. Test the significance at 0.05 level. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842877 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=842877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 49.<BR>\n" );
document.write( "sample mean is 15200.<BR>\n" );
document.write( "population mean is 15150.<BR>\n" );
document.write( "population standard deviation is 1200.<BR>\n" );
document.write( "confidence interval is .95\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "standard error = standard deviation / sqrt(sample size) = 1200 / sqrt(49) = 171.4285714\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z-score formula is z = (x-m)/s<BR>\n" );
document.write( "z = the z-score<BR>\n" );
document.write( "x = the sample mean<BR>\n" );
document.write( "m = the population mean<BR>\n" );
document.write( "s = the standard error\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "formula becomes:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "z = (15200 - 15150) / 171.4285714 = .291666667.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "area to the right of that z-score is equal to .3853.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is much greater than the critical p-value of .05/2 = .025.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this indicates the results are not significant and that the sample mean is clearly within the confidence limits and therefore it is quite possible to get a sample mean of 15200 when the population mean is 15150.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "here are the results using an online calculator with the population mean of 15150 and the standard error of 171.4285714.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2024/012621.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );