document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=179742>Question 179742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 10.24 - 10.24 Below is a random sample of shoe sizes for 12 mothers and their daughters. (a) At &#945; = .01, does this sample show that women’s shoe sizes have increased? State your hypotheses and show all steps clearly. (b) Is the decision close? (c) Are you convinced? (d) Why might shoe sizes change<BR>\n" );
document.write( "over time? (See The Wall Street Journal, July 17, 2004.) Shoe Size 2\r<BR>\n" );
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document.write( "         1  2   3   4  5    6     7   8    9  10  11  12<BR>\n" );
document.write( "Daughter 8  8  7.5  8  9    9    8.5  9    9  8   7   8<BR>\n" );
document.write( "Mother   7  7  7.5  8  8.5  8.5  7.5  7.5  6  8   7   7 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #134642 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=134642\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Below is a random sample of shoe sizes for 12 mothers and their daughters.<BR>\n" );
document.write( "Daughter 8 8 7.5 8 9 9 8.5 9 9 8 7 8<BR>\n" );
document.write( "d-bar = 8.25 ; s = 0.657<BR>\n" );
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document.write( "Mother 7 7 7.5 8 8.5 8.5 7.5 7.5 6 8 7 7<BR>\n" );
document.write( "m-bar = 7.46 ; s = 0.721<BR>\n" );
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document.write( "(a) At &#945; = .01, does this sample show that women’s shoe sizes have increased? State your hypotheses and show all steps clearly.<BR>\n" );
document.write( "Ho: ud-um = 0<BR>\n" );
document.write( "Ha: ud-um < 0 (this for a right-tail test; you could reverse the inequality<BR>\n" );
document.write( "and make a left tail test)<BR>\n" );
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document.write( "Critical Value: z = 2.326...<BR>\n" );
document.write( "Test statistic: z(8.25-7.46) = (0.79)/sqrt[(0.657)^2/12 + (0.721)^2/12] = 2.81<BR>\n" );
document.write( "p-value: P(z>2.81) = 0.0025<BR>\n" );
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document.write( "Conclusion: Since p-value < 1%, reject Ho.<BR>\n" );
document.write( "daughter's sizes are greater than mother's sizes<BR>\n" );
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document.write( "(b) Is the decision close? <BR>\n" );
document.write( "No.   Less than (1/4) of 1% of test results could have provided stronger<BR>\n" );
document.write( "evidence for rejecting Ho.<BR>\n" );
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document.write( "(c) Are you convinced? <BR>\n" );
document.write( "Yes<BR>\n" );
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document.write( "(d) Why might shoe sizes change over time? <BR>\n" );
document.write( "They don't; foot sizes change.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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