document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=385495>Question 385495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During<BR>\n" );
document.write( "a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of<BR>\n" );
document.write( "yellow fire trucks made 135,035 runs and had 4 accidents. At &#945; = .01, did the yellow fire trucks<BR>\n" );
document.write( "have a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule and<BR>\n" );
document.write( "sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the<BR>\n" );
document.write( "p-value and interpret it. (f ) If statistically significant, do you think the difference is large enough to<BR>\n" );
document.write( "be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.\r<BR>\n" );
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document.write( "My question is...I don't know where to start. How do I know what formula to use? To find the z value, excel wants variable ranges. ?? How do I find the sample proportions?\r<BR>\n" );
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document.write( "I am in a crunch situation and need the answers, but I also want to know how to do the problems.\r<BR>\n" );
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document.write( "Thanks\r<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 #272741 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=272741\">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,<BR>\n" );
document.write( "p-hat(red) = 20/153,348 = 0.0001304<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" );
document.write( "p-hat(yellow) = 4/135,035 = 0.00002962<BR>\n" );
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document.write( "Difference of sample proportions: 0.0001006<BR>\n" );
document.write( "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 is z > 2.326<BR>\n" );
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document.write( "(c) Find the sample proportions and z test statistic.<BR>\n" );
document.write( "Using a TI calculator for a 2-Proportion Z-Test I get<BR>\n" );
document.write( "z = 2.961\r<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(z>2.961) = 0.0015..<BR>\n" );
document.write( "0.015% of test results could have given stronger evidence for 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( "I'll leave that to you.<BR>\n" );
document.write( "Looks like yellow wins.<BR>\n" );
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document.write( "(g) Is the normality assumption fulfilled? Explain <BR>\n" );
document.write( "Independence and x < 10%<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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