document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=145859>Question 145859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please, help me with these questions, Thanks.\r<BR>\n" );
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document.write( "  1.         Nancy Giggles has not been doing well on statistics examinations. She decides to sample 12 of her friends to determine the number of hours spent studying for Test 3 and the score out of 100 received on that test. The results: \r<BR>\n" );
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document.write( "Test 4 Score<BR>\n" );
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document.write( " Hours of study<BR>\n" );
document.write( " <BR>\n" );
document.write( "47<BR>\n" );
document.write( " 7<BR>\n" );
document.write( " <BR>\n" );
document.write( "55<BR>\n" );
document.write( " 10<BR>\n" );
document.write( " <BR>\n" );
document.write( "87<BR>\n" );
document.write( " 39<BR>\n" );
document.write( " <BR>\n" );
document.write( "98<BR>\n" );
document.write( " 43<BR>\n" );
document.write( " <BR>\n" );
document.write( "37<BR>\n" );
document.write( " 2<BR>\n" );
document.write( " <BR>\n" );
document.write( "71<BR>\n" );
document.write( " 12<BR>\n" );
document.write( " <BR>\n" );
document.write( "100<BR>\n" );
document.write( " 51<BR>\n" );
document.write( " <BR>\n" );
document.write( "98<BR>\n" );
document.write( " 48<BR>\n" );
document.write( " <BR>\n" );
document.write( "85<BR>\n" );
document.write( " 23<BR>\n" );
document.write( " <BR>\n" );
document.write( "82<BR>\n" );
document.write( " 26<BR>\n" );
document.write( " <BR>\n" );
document.write( "56<BR>\n" );
document.write( " 7<BR>\n" );
document.write( " <BR>\n" );
document.write( "78<BR>\n" );
document.write( " 14<BR>\n" );
document.write( " \r<BR>\n" );
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document.write( "(i)                 Find the equation of the regression line using the least square technique.  Interpret the meanings conveyed by the regression equation. \r<BR>\n" );
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document.write( "(ii)               Compute the correlation coefficient and the coefficient of Determination.  Interpret these values. \r<BR>\n" );
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document.write( "2.         David Gallano, a wine merchant, has selected opinions on grape wine quality from a random sample of his customers.  The customers tasted wine made from grapes grown in three regions of the country.  The customers rated wine quality on a scale of 1 (best) to 4 (worst).  The sample data looks like:\r<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "Customer Quality Rating of Wine by Grape-growing region\r<BR>\n" );
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document.write( "Quality Rating\r<BR>\n" );
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document.write( " Growing Region\r<BR>\n" );
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document.write( "I<BR>\n" );
document.write( " Growing Region\r<BR>\n" );
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document.write( "II Growing Region\r<BR>\n" );
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document.write( "III<BR>\n" );
document.write( " Row Total <BR>\n" );
document.write( "1<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 10<BR>\n" );
document.write( " 6<BR>\n" );
document.write( " 31<BR>\n" );
document.write( " <BR>\n" );
document.write( "2<BR>\n" );
document.write( " 7<BR>\n" );
document.write( " 13<BR>\n" );
document.write( " 12<BR>\n" );
document.write( " 32<BR>\n" );
document.write( " <BR>\n" );
document.write( "3<BR>\n" );
document.write( " 11<BR>\n" );
document.write( " 12<BR>\n" );
document.write( " 8<BR>\n" );
document.write( " 31<BR>\n" );
document.write( " <BR>\n" );
document.write( "4<BR>\n" );
document.write( " 3<BR>\n" );
document.write( " 8<BR>\n" );
document.write( " 15<BR>\n" );
document.write( " 26<BR>\n" );
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document.write( "Column Total<BR>\n" );
document.write( " <BR>\n" );
document.write( " 36<BR>\n" );
document.write( " 43<BR>\n" );
document.write( " 41<BR>\n" );
document.write( " 120<BR>\n" );
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document.write( " \r<BR>\n" );
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document.write( "David wants to know whether quality ratings are independent of the grape-growing region.  Can you conclude at a 95% confidence that the quality rating is independent of the growing region?<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 #106454 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=106454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Nancy Giggles has not been doing well on statistics examinations. She decides to sample 12 of her friends to determine the number of hours spent studying for Test 3 and the score out of 100 received on that test. The results: <BR>\n" );
document.write( "Test 4 Score Hours of study<BR>\n" );
document.write( "47 7<BR>\n" );
document.write( "55 10<BR>\n" );
document.write( "87 39<BR>\n" );
document.write( "98 43<BR>\n" );
document.write( "37 2<BR>\n" );
document.write( "71 12<BR>\n" );
document.write( "100 51<BR>\n" );
document.write( "98 48<BR>\n" );
document.write( "85 23<BR>\n" );
document.write( "82 26<BR>\n" );
document.write( "56 7<BR>\n" );
document.write( "78 14 <BR>\n" );
document.write( "(i) Find the equation of the regression line using the least square technique. Interpret the meanings conveyed by the regression equation.<BR>\n" );
document.write( "test score = 1.1128(hrs of study) + 48.35..<BR>\n" );
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document.write( "(ii) Compute the correlation coefficient and the coefficient of Determination. Interpret these values.<BR>\n" );
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document.write( "r = 0.918168...<BR>\n" );
document.write( "r is a measure of the strength of the linear relationship between the variables.<BR>\n" );
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document.write( "r^2 = 0.8430...<BR>\n" );
document.write( "84.3% of the variability in the test scores is explained by the regression equation.<BR>\n" );
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document.write( "2. David Gallano, a wine merchant, has selected opinions on grape wine quality from a random sample of his customers. The customers tasted wine made from grapes grown in three regions of the country. The customers rated wine quality on a scale of 1 (best) to 4 (worst). The sample data looks like: <BR>\n" );
document.write( "Customer Quality Rating of Wine by Grape-growing region<BR>\n" );
document.write( "Quality Rating<BR>\n" );
document.write( "Growing Region<BR>\n" );
document.write( "I Growing Region II Growing Region III Row Total<BR>\n" );
document.write( "1 15 10 6 31<BR>\n" );
document.write( "2 7 13 12 32<BR>\n" );
document.write( "3 11 12 8 31<BR>\n" );
document.write( "4 3 8 15 26<BR>\n" );
document.write( "Column Total<BR>\n" );
document.write( "36 43 41 120 <BR>\n" );
document.write( "David wants to know whether quality ratings are independent of the grape-growing region. Can you conclude at a 95% confidence that the quality rating is independent of the growing region?<BR>\n" );
document.write( "Ho: they are independent<BR>\n" );
document.write( "Ha: they are dependent<BR>\n" );
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document.write( "I ran a Chi-Sq on the 4 x 3 set of data and got the following results:<BR>\n" );
document.write( "Chi-Sq = 14.9760...<BR>\n" );
document.write( "p-value = 0.02044...<BR>\n" );
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document.write( "Conclusion: Since p-value is less than 5%, reject Ho.<BR>\n" );
document.write( "The quality rating and growing region are dependent variables.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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