document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1025445>Question 1025445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> an economist claims that the mean family income of a certain populated area in metro manila at most is 22,450.00 a year. <BR>\n" );
document.write( "test the claim at 0.05 level of significance the economics students take a sample of 150 families obtaining a mean of 19,769.00 with standard deviation of 529.00 what is the conclusion </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #640706 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=640706\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> claim is that the mean family income is at most 22,450 per year.\r<BR>\n" );
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document.write( "sample taken.<BR>\n" );
document.write( "mean of sample is 19769.<BR>\n" );
document.write( "standard deviation of sample is 529.<BR>\n" );
document.write( "sample size is 150.\r<BR>\n" );
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document.write( "standard error is equal to standard deviation divided by square root of sample size.\r<BR>\n" );
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document.write( "standard error is therefore equal to 529 / sqrt(150) = 43.19 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "sample mean is 19769.<BR>\n" );
document.write( "standard error of the mean, which is also referred to as the standard deviation of the distribution of sample means, is equal to 43.19.\r<BR>\n" );
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document.write( "at 5% level of significance, you would expect the z-score to be between -1.96 and 1.96 for 95% of the samples taken.\r<BR>\n" );
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document.write( "this means the the sample mean would be between 19769 - 1.96 * 43.19 and 19769 + 1.96 * 43.19 for 95% of the sample taken.\r<BR>\n" );
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document.write( "this would put the sample mean between 19684.35 and 19853.65 for 95% of the sample taken.\r<BR>\n" );
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document.write( "this is well below the claimed maximum mean of 22450.\r<BR>\n" );
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document.write( "the claim is therefore supported.\r<BR>\n" );
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document.write( "it's not even close.\r<BR>\n" );
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document.write( "each of the sample is assumed to have the same sample size of 150.\r<BR>\n" );
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