document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=175835>Question 175835</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. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #131099 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=131099\">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(yel) = 0<BR>\n" );
document.write( "Ha: p(red)-p(yel) > 0<BR>\n" );
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document.write( "(b) State the decision rule and sketch it.<BR>\n" );
document.write( "Critical Value z = 2.3263 ; If T.S. > 2.3263,reject Ho.<BR>\n" );
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document.write( "(c) Find the sample proportions and z test statistic.<BR>\n" );
document.write( "P-hat(red) 20/153,035; p-hat(yel)=4/135,035<BR>\n" );
document.write( "T.S. : z(diff) = 2.9610<BR>\n" );
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document.write( "(d) Make a decision.<BR>\n" );
document.write( "Reject Ho since T.S. > C.R.<BR>\n" );
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document.write( "(e) Find the p-value and interpret it.<BR>\n" );
document.write( "p-value = P(z>2.9610) = 0.0015..<BR>\n" );
document.write( "Only 0.1% of test results could have given stronger support 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( "My opinion: Yes<BR>\n" );
document.write( "Your opinion: ?<BR>\n" );
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document.write( "(g) Is the normality assumption fulfilled? Explain.<BR>\n" );
document.write( "Check your text.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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