document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127648>Question 127648</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh>Applie Statics in Business and Econmics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I have been working with someone else on this problem and we are both stuck. Can you please give any help to this problem. Thanks so much!!!!<BR>\n" );
document.write( "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 trucks made 135, 035 rund and had 4 accidents. <BR>\n" );
document.write( "At a=.01, did the yellow fire trucks have a significantly lower accident rate?<BR>\n" );
document.write( "A. State the hypotheses.<BR>\n" );
document.write( "B. State the decision rule and sketch it.<BR>\n" );
document.write( "C. Find the sample proportions and z test statistic.<BR>\n" );
document.write( "D. Make a decision.<BR>\n" );
document.write( "E. Find the p-value and interpret it.<BR>\n" );
document.write( "F. If statistically significant, do you think the difference is large enough to be imporant? if so, to whom, and why?<BR>\n" );
document.write( "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 #93645 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=93645\">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" );
document.write( "During 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( "-------<BR>\n" );
document.write( "p-hat(red) = 20/153,348 = 1.304x10^-4<BR>\n" );
document.write( "------------<BR>\n" );
document.write( "yellow fire trucks made 135,035 runs and had 4 accidents. <BR>\n" );
document.write( "p-hat(yellow) = 4/135035 = 2.9622x10-5<BR>\n" );
document.write( "-------------------<BR>\n" );
document.write( "At &#945; = .01, did the yellow fire trucks have a significantly lower accident rate?<BR>\n" );
document.write( "One-tail z-test: Critical value = 2.326<BR>\n" );
document.write( "(a) State the hypothesis.<BR>\n" );
document.write( "Ho: p(red)-p(yellow) = 0<BR>\n" );
document.write( "Ha: p(red)-p(yellow) < 0<BR>\n" );
document.write( "-------------------------------<BR>\n" );
document.write( "(b) State the decision rule and sketch it.<BR>\n" );
document.write( "? Not sure what is meant by this.<BR>\n" );
document.write( "------------------------------- <BR>\n" );
document.write( "(c) Find the sample proportions and z test statistic.<BR>\n" );
document.write( "Test statistic:<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Note: p-bar= (4+20)/(153348+135035) = 8.3223x10^-5;q-bar=1-p-bar<BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Test statistic<BR>\n" );
document.write( "z(1.0078x10^-4) = 1.0078x10^-4/sqrt[(p-bar)(q-bar)/n1 + (p-bar)(q-bar)/n2]<BR>\n" );
document.write( "= 2.9610 <BR>\n" );
document.write( "(d) Make a decision.<BR>\n" );
document.write( "Since the test statistic is greater than the critical value, reject Ho.<BR>\n" );
document.write( "p(red) is not equal to p(yellow)<BR>\n" );
document.write( "------------------------------------------ <BR>\n" );
document.write( "(e) Find the p-value and interpret it.<BR>\n" );
document.write( "p-value = 0.0015 ; Only 0.15% of test results could have provided stronger<BR>\n" );
document.write( "evidence for rejecting Ho.\r<BR>\n" );
document.write( "\n" );
document.write( "------------------------- <BR>\n" );
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( "--------------------<BR>\n" );
document.write( "(g) Is the normality assumption fulfilled? Explain.<BR>\n" );
document.write( "Show that p(red)n1>5, q(red)n1>5 <BR>\n" );
document.write( "and p(yellow)n2>5, q(yellow)n2>5<BR>\n" );
document.write( "=======================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );