document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188881>Question 188881</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SafeRoad Stores is redesigning the checkout lanes in its stores throughout the country. Two designs have been suggested. Tests on customer checkout times have been conducted at two stores where the two new systems have been installed. A summary of the sample data follows:\r<BR>\n" );
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document.write( "System A	<BR>\n" );
document.write( "Sample size = 25	<BR>\n" );
document.write( "Sample mean checking out time = 4.3 minutes	<BR>\n" );
document.write( "Sample standard deviation = 2.0 minutes	\r<BR>\n" );
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document.write( "System B<BR>\n" );
document.write( "Sample size = 25<BR>\n" );
document.write( "Sample mean checkout time = 3.3 minutes<BR>\n" );
document.write( "Sample standard deviation = 3.0 minutes\r<BR>\n" );
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document.write( "At the 0.05 significance level, perform a statistical test to see the two systems are significantly different.<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 #141657 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=141657\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ----------<BR>\n" );
document.write( "SafeRoad Stores is redesigning the checkout lanes in its stores throughout the country. Two designs have been suggested. Tests on customer checkout times have been conducted at two stores where the two new systems have been installed. A summary of the sample data follows: \r<BR>\n" );
document.write( "\n" );
document.write( "System A <BR>\n" );
document.write( "Sample size = 25 <BR>\n" );
document.write( "Sample mean checking out time = 4.3 minutes <BR>\n" );
document.write( "Sample standard deviation = 2.0 minutes<BR>\n" );
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document.write( "System B<BR>\n" );
document.write( "Sample size = 25<BR>\n" );
document.write( "Sample mean checkout time = 3.3 minutes<BR>\n" );
document.write( "Sample standard deviation = 3.0 minutes<BR>\n" );
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document.write( "At the 0.05 significance level, perform a statistical test to see the two systems are significantly different.<BR>\n" );
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document.write( "Ho: u(A) - u(B) = 0<BR>\n" );
document.write( "Ha: u(A) - u(B) is not equal to zero<BR>\n" );
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document.write( "Critical t-values for 2-tail test with alpha = 5%: z = +/-1.96 <BR>\n" );
document.write( "test statistic: z(4.3-3.3) = (4.4-3.3)/sqrt[(2^2/25) + (3^2/25] = 1.5254<BR>\n" );
document.write( "p-value = 2P(z > 1.5254) = 0.1272<BR>\n" );
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document.write( "Conclusion: Since the p-value is greater than 5%, fail to reject Ho.<BR>\n" );
document.write( "The checkout times are not the same with the two systmes.<BR>\n" );
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document.write( "Comment:  Now you need to understand every piece of this solution.<BR>\n" );
document.write( "If you do you can work any problem comparing two sample means. <BR>\n" );
document.write( "sample means.<BR>\n" );
document.write( "Ask if you do not understand ; it is the only way to learn.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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