document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201206>Question 1201206</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In October, the campus bookstore asked a random set of freshmen and seniors how much they had spent on textbooks that semester. The bookstore believes that the two groups spent the same amount. What is an appropriate test value for a z test?\r<BR>\n" );
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document.write( "Sample size:  freshmen 50, seniors 60<BR>\n" );
document.write( "Sample mean freshmen $480, seniors $500<BR>\n" );
document.write( "Population std.dev. freshmen $52, seniors $63<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 #837543 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=837543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> since you know the population standard deviation, i believe you can use the z-score.<BR>\n" );
document.write( "note that the sample size is greater than 30 as well.\r<BR>\n" );
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document.write( "here's a refernce on when to use t-score versus when to use z-score.<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value\" target = \"_blank\">https://math.stackexchange.com/questions/1817980/how-to-know-when-to-use-t-value-or-z-value</a>\r<BR>\n" );
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document.write( "freshmen:<BR>\n" );
document.write( "sample size is 50<BR>\n" );
document.write( "sample mean is 480<BR>\n" );
document.write( "population standard deviation is 52\r<BR>\n" );
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document.write( "seniors:<BR>\n" );
document.write( "sample size is 60<BR>\n" );
document.write( "sample mean is 500<BR>\n" );
document.write( "population standard deviation is 63\r<BR>\n" );
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document.write( "standard error of the test is sqrt(52^2/50 + 63^2/60) = 10.964974414.\r<BR>\n" );
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document.write( "mean difference is 20<BR>\n" );
document.write( "standard error is 10.964974414<BR>\n" );
document.write( "z-score is 20 / that = 1.8239947\r<BR>\n" );
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document.write( "critical z-score for 95% two tailed confidence interval is equal to plus or minus 1.96<BR>\n" );
document.write( "since test z-score is within these limits, the results are not significant and the conclusion is that the means of the two samples are not considered to be different.<BR>\n" );
document.write( "if you want to use p-value, then:<BR>\n" );
document.write( "the two-tailed p-value is .034 * 2 (.034 on the left and .034 on the right) which is equal to .068 which is greater than two tailed critical p-value of .05.<BR>\n" );
document.write( "note that the two tailed critical p-value is divided by 2 to get a p-value of .025 on each end.\r<BR>\n" );
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document.write( "here are the results from the calculator i found at <a  rel=nofollow HREF= \"https://www.statskingdom.com/120MeanNormal2.html\" target = \"_blank\">https://www.statskingdom.com/120MeanNormal2.html</a> that confirms these results.\r<BR>\n" );
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