document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132942>Question 132942</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh>Applied Statistics in Business and Economics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility.During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents,while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At a =.01,did the yellow fire trucks have a significantly lower accident rate?(a)State the hypothesis.(b)State the decision rule and sketch it.(c)Find the sample proportions and z test statistic.(d)Make a decision.(e)Find the p-value and interpret it.(f)If statistically significant,do you think the difference is large enough to be important?If so,to whom,and why?(g)Is the normality assumption fulfilled?Explain. <BR>\n" );
document.write( "Accident Rate for Dallas Fire Trucks <BR>\n" );
document.write( "Statistic               Red Fire Trucks      Yellow Fire Trucks <BR>\n" );
document.write( "No. of accidents        X,=20 accidents       X2=4 accidents                    No. of fire runs         N,=153,348 runs      N2=135,035 runs  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #97441 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=97441\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility.<BR>\n" );
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document.write( "During the test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents,<BR>\n" );
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document.write( "while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents.<BR>\n" );
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document.write( "At a=.01, did the yellow fire trucks have a significantly lower accident rate?<BR>\n" );
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document.write( "a) State the hypothesis<BR>\n" );
document.write( "Ho: p-hat(red)-p-hat(yellow <=0<BR>\n" );
document.write( "Ha: p-hat(red)-p-hat(yellow) > 0<BR>\n" );
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document.write( "b) State the decision rule and sketch it.<BR>\n" );
document.write( "Critical value for one-tail z-test with alpha=1% = 2.326<BR>\n" );
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document.write( "c) Find the sample proportions and = test statistic<BR>\n" );
document.write( "Using a TI Calculator and running a 2-Proportion Z-Test I get:<BR>\n" );
document.write( "p-hat(red)= 0.0001304223; p-hat(yellow)=0.00002982195<BR>\n" );
document.write( "Pooled p-hat = 0.000032226598<BR>\n" );
document.write( "test statistic = 2.960988745<BR>\n" );
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document.write( "d) Make a decision<BR>\n" );
document.write( "Since test stat is greater than critical value, reject Ho.<BR>\n" );
document.write( "There were statistically more accidents with the red than with the yellow vehicles.<BR>\n" );
document.write( "e) Find the p-value and interpret it<BR>\n" );
document.write( "p-value = 0.0015333...; Only 0.0015333 of test results could have shown<BR>\n" );
document.write( "stronger evidence that the red had a higher accident rate than the yellow.<BR>\n" );
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document.write( "f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?<BR>\n" );
document.write( "Yes, the test gave strong evidence that painting the trucks yellow <BR>\n" );
document.write( "reduced the accident rate.<BR>\n" );
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document.write( "g) 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.\r<BR>\n" );
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