document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=260300>Question 260300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Do a larger proportion of college students than young children eat cereal? Researchers surveyed<BR>\n" );
document.write( "both age groups to find the answer. The results are shown in the table below. \r<BR>\n" );
document.write( "\n" );
document.write( "(a) State the hypotheses used to answer the question.<BR>\n" );
document.write( " (b) Using &#945; = .05, state the decision rule and sketch it.<BR>\n" );
document.write( "(c) Find the sample proportions and z statistic.<BR>\n" );
document.write( " (d) Make a decision.<BR>\n" );
document.write( " (e) Find the p-value and interpret it<BR>\n" );
document.write( "(f ) Is the normality assumption fulfilled? Explain.\r<BR>\n" );
document.write( "\n" );
document.write( "Statistic	                  College Students            Young Children<BR>\n" );
document.write( "                                   (ages 18-25)                 (ages 6-11)<BR>\n" );
document.write( "Number who eat cereal	                 x1=833	                  x2=692<BR>\n" );
document.write( "Number surveyed	                         n1=850	                  n2=740<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #191753 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=191753\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Do a larger proportion of college students than young children eat cereal? Researchers surveyed both age groups to find the answer. <BR>\n" );
document.write( "The results are shown in the table below. <BR>\n" );
document.write( "-------------------------------------------------------------<BR>\n" );
document.write( "(a) State the hypotheses used to answer the question.<BR>\n" );
document.write( "Ho: p(college)-p(children) = 0<BR>\n" );
document.write( "Ha: p(coll)-p(chil) > 0<BR>\n" );
document.write( "------------------------------------\r<BR>\n" );
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document.write( "(b) Using alpha = .05, state the decision rule and sketch it.<BR>\n" );
document.write( "Reject Ho if z > 1.645<BR>\n" );
document.write( "---------------------------<BR>\n" );
document.write( "(c) Find the sample proportions and z statistic.<BR>\n" );
document.write( "Phat(col) = 0.98 ; phat(chil) = -.935<BR>\n" );
document.write( "test stat = z = 4.5065<BR>\n" );
document.write( "p-value = p(z> 4.5065) = 0.000003298...<BR>\n" );
document.write( "----------------------------------------<BR>\n" );
document.write( "(d) Make a decision.<BR>\n" );
document.write( "Since the p-value is so small, reject Ho; the proportions are not equal.<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "(e) Find the p-value and interpret it<BR>\n" );
document.write( "(f) Is the normality assumption fulfilled? Explain.<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
document.write( "=================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( "Statistic	                  College Students            Young Children<BR>\n" );
document.write( "                                   (ages 18-25)                 (ages 6-11)<BR>\n" );
document.write( "Number who eat cereal	                 x1=833	                  x2=692<BR>\n" );
document.write( "Number surveyed	                         n1=850	                  n2=740<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );