document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146066>Question 146066</A>: <I><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. The results are shown in the table below. (a) State the hypotheses used to answer the question. (b) Using &#945; = .05, state the decision rule and sketch it. (c) Find the sample proportions and z statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f) Is the normality assumption fulfilled? Explain \r<BR>\n" );
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document.write( "Statistic	College Students (ages 18–25)	Young Children (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 #106623 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=106623\">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. The results are shown in the table below.<BR>\n" );
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document.write( "Statistic College Students<BR>\n" );
document.write( "........ (ages 18–25) Young Children (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" );
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document.write( "(a) State the hypotheses used to answer the question.<BR>\n" );
document.write( "Ho: p(college) - p(youngsters) = 0<BR>\n" );
document.write( "Ha: p(college) - p(youngsters) > 0<BR>\n" );
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document.write( "(b) Using &#945; = .05, state the decision rule and sketch it.<BR>\n" );
document.write( "Reject Ho if z> 1.645<BR>\n" );
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document.write( " (c) Find the sample proportions and z statistic.<BR>\n" );
document.write( "p1-hat = 833/850 = 0.98.. ; p2-hat = 692/740 = 0.9351...<BR>\n" );
document.write( "p-bar = (833+692)/(850+740) = 0.95912..<BR>\n" );
document.write( "I  ran a 2-proportion Z-test on a TI calculator to get:<BR>\n" );
document.write( "z(0.98-09351) = 4.50649...<BR>\n" );
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document.write( "(d) Make a decision. <BR>\n" );
document.write( "Since 4.50649.. is greater than 1.645, reject Ho.<BR>\n" );
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document.write( "(e) Find the p-value and interpret it.<BR>\n" );
document.write( "p-value = 0.000003298...<BR>\n" );
document.write( "Only that percentage of test results could have resulted in stronger<BR>\n" );
document.write( "evidence for rejecting Ho.<BR>\n" );
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document.write( "(f) Is the normality assumption fulfilled? Explain<BR>\n" );
document.write( "I'll leave that to you.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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