document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=246044>Question 246044</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A department store management claims that families spend an average of $630 on gifts during the Christmas season. A sample of 105 families showed  that they spent an average of $660 on gifts during the past Christmas season with a standard deviation of $165. Test that the 5% significance level if the mean amount spent on gifts during the holiday by all families is different from $630.(could you please show all 8 steps). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #179721 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=179721\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A department store management claims that families spend an average of $630 on gifts during the Christmas season. <BR>\n" );
document.write( "A sample of 105 families showed that they spent an average of $660 on gifts during the past Christmas season with a standard deviation of $165. <BR>\n" );
document.write( "Test at the 5% significance level if the mean amount spent on gifts during the holiday by all families is different from $630.<BR>\n" );
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document.write( "Ho: u = 630<BR>\n" );
document.write( "H1: u is not equal to 630<BR>\n" );
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document.write( "CV: 2-tail test at 5% with df = 104: t = +/-1.983<BR>\n" );
document.write( "TS: t(660) = (660-630)/[165/sqrt(105)] = 1.8631<BR>\n" );
document.write( "p-value = 2*P(t>1.8631 with df=104) = 2(0.0326) = 0.0653<BR>\n" );
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document.write( "Conclusion:  Since the p-value is greater than 5%, fail to <BR>\n" );
document.write( "reject Ho. The mean amount spent is different from $630.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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