document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1137774>Question 1137774</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The treasurer of a municipality claims that the average net worth of families in this municipality is 730,000.00php. a random sample of 50 families selected from this area produced a mean net worth of 860,000.00php. with standard deviation  of 65,000.00php. using 0.1 significance level, can we conclude that the claim is true? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #755669 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=755669\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean is 730,000.\r<BR>\n" );
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document.write( "sample size is 50.\r<BR>\n" );
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document.write( "sample mean is 860,000.\r<BR>\n" );
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document.write( "sample standard deviation is 65,000.\r<BR>\n" );
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document.write( "since you do not have the population standard deviation, i believe you need to find the t-score rather than the z-score.\r<BR>\n" );
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document.write( "since the sample size is quite large, the z-score would probably be close.\r<BR>\n" );
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document.write( "using the z-score, you would get z = (860,000 - 730,000) / s\r<BR>\n" );
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document.write( "s is the stnadard error which is equal to standard deviation of the sample in this case divided by the square root of the sample size.\r<BR>\n" );
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document.write( "that makes s = 65,000 / sqrt(50) = 9192.388155.\r<BR>\n" );
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document.write( "the z-score is therefore (860,000 - 730,000) / 9192.388155 = 14.14213562.\r<BR>\n" );
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document.write( "the critical z-score at 1% significance level is either 1.2i8... if it's a one tail distributuion, or 1.645... if it's a two tail distributuion.\r<BR>\n" );
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document.write( "in either case, a z-score of 14 + is so far behyond this that there is no way the population average could be 730,000 if the sample average of 50 families is 860,000.\r<BR>\n" );
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document.write( "if you do this using t-scores, you'll get a similar answer because the sample size is quite large, making the t-score get pretty close to the z-score.\r<BR>\n" );
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document.write( "the critical t-score with 49 degrees of freedom and .1 significance level is somewhere between 1.303 and 1.296 for a tone tail distribution and somewhere between 1.684 and 1.671 for a two tail distribution.\r<BR>\n" );
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document.write( "a t-score of 14 + is way beyond this as well.\r<BR>\n" );
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document.write( "you would have to reject the claim that the population average is 730,000 based on the results of the sample taken.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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