document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206358>Question 206358</A>: <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 &#945; = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypotheses. (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.\r<BR>\n" );
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document.write( "Statistic Red Fire Trucks Yellow Fire Trucks<BR>\n" );
document.write( "Number of accidents x1 = 20 accidents x2 = 4 accidents<BR>\n" );
document.write( "Number of fire runs n1 = 153,348 runs n2 = 135,035 runs<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 #155940 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=155940\">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. 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 &#945; = .01, did the yellow fire trucks have a significantly lower accident rate? <BR>\n" );
document.write( "(a) State the hypotheses. <BR>\n" );
document.write( "Ho: p(red)-p(yellow) = 0<BR>\n" );
document.write( "Ha: p(red)-p(yellow) > 0<BR>\n" );
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document.write( "(b) State the decision rule and sketch it. <BR>\n" );
document.write( "Reject Ho if the test statistic is greater than z = 2.3263<BR>\n" );
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document.write( "(c) Find the sample proportions and z test statistic.<BR>\n" );
document.write( "p-hat(red) = 20/153348 ; p-hat(yellow) = 4/135,035 <BR>\n" );
document.write( "z-test statistic: 2.961<BR>\n" );
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document.write( "(d) Make a decision. <BR>\n" );
document.write( "Reject Ho<BR>\n" );
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document.write( "(e) Find the p-value and interpret it. <BR>\n" );
document.write( "p-value: P(z>2.961) = 0.0015<BR>\n" );
document.write( "Only 0.15% of test results could provide stronger evidence for<BR>\n" );
document.write( "rejecting Ho.<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, it supports painting all engines yellow<BR>\n" );
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document.write( "(g) Is the normality assumption fulfilled? Explain.<BR>\n" );
document.write( "The sample sizes are large enough to support the conclusion.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "Statistic Red Fire Trucks Yellow Fire Trucks<BR>\n" );
document.write( "Number of accidents x1 = 20 accidents x2 = 4 accidents<BR>\n" );
document.write( "Number of fire runs n1 = 153,348 runs n2 = 135,035 runs<BR>\n" );
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