document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=918897>Question 918897</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Based on historical information, it is assumed that no more than 35% <BR>\n" );
document.write( "of aggregate household income is spent on food. A researcher believes <BR>\n" );
document.write( "that this proportion is now lower with increase in real wages. A study of <BR>\n" );
document.write( "82 persons show that 37 spend less than 35%, is there reason at the <BR>\n" );
document.write( "5% significance level to believe that the proportion is now lower?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #557296 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=557296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Based on historical information, it is assumed that no more than 35% <BR>\n" );
document.write( "of aggregate household income is spent on food. A researcher believes <BR>\n" );
document.write( "that this proportion is now lower with increase in real wages. A study of <BR>\n" );
document.write( "82 persons show that 37 spend less than 35%, is there reason at the <BR>\n" );
document.write( "5% significance level to believe that the proportion is now lower?<BR>\n" );
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document.write( "Ho: p >= 0.35<BR>\n" );
document.write( "Ha: p < 0.35 (claim)<BR>\n" );
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document.write( "p-hat = 37/82 = 0.82<BR>\n" );
document.write( "test stat:: z(0.82) = (0.82-0.35)/sqrt[0.35*0.65/82] = 15.56 (that's enormous)<BR>\n" );
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document.write( "p-value = p(z > 15.56) = 0<BR>\n" );
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document.write( "Conclusion:: Since the p-value is less than 5%, reject Ho.<BR>\n" );
document.write( "The test results support the claim.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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