document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192947>Question 1192947</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 16. Ford Motor Company claims that its new 8-cylinder sedan, the XSG, will average 24 miles per gallon.<BR>\n" );
document.write( "Recently, on the blog Ford#1, the show’s host collected sample gas mileage information randomly from 29<BR>\n" );
document.write( "XSG owners who follow the blog. The sample revealed a mean of 21.5 mpg with standard deviation 1.9 mpg. Use correct symbols. AND THEN Compute the sample mean and standard deviation.\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 #825096 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=825096\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population mean is assumed to be 24.<BR>\n" );
document.write( "sample mean is 21.5<BR>\n" );
document.write( "sample standard deviation is 1.9.<BR>\n" );
document.write( "sample size is 29.\r<BR>\n" );
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document.write( "standard error is 1.9 / sqrt(29) = .352821 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "the formula becomes z = (21.5 - 24) / .352821 = -7.08574603.\r<BR>\n" );
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document.write( "the area to the left of that z-score is equal to 0.\r<BR>\n" );
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document.write( "what this says is that the probability you would get a z-score less than -7.08..... is so small as it is effectively equal to 0.\r<BR>\n" );
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document.write( "here's a reference on symbols.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.dummies.com/article/academics-the-arts/math/statistics/seeing-what-statistical-symbols-stand-for-142633/\" target = \"_blank\">https://www.dummies.com/article/academics-the-arts/math/statistics/seeing-what-statistical-symbols-stand-for-142633/</a>\r<BR>\n" );
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document.write( "note that, because you are using the sample standard deviation rather than the population standard deviation, you would probably be using the t-stoce rather than the z-score.\r<BR>\n" );
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document.write( "the t-score itself is calculated in the same way as the z-score.\r<BR>\n" );
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document.write( "the difference is in the area under the normal distribution curve to the left or right of the t-score as opposed to the area to the left or right of the z-score.\r<BR>\n" );
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document.write( "t-scores use degrees of freedom whereas z-score don't.\r<BR>\n" );
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document.write( "the degrees of freedom are usually 1 less than the sample size.\r<BR>\n" );
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document.write( "if the degrees of freedom are small, there is a larger difference between the area to the left or right of a t-score compared to the area to the left or right of a z-score.\r<BR>\n" );
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document.write( "some examples:\r<BR>\n" );
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document.write( "z-score = -1<BR>\n" );
document.write( "area to the left = .158655\r<BR>\n" );
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document.write( "t-score with 5 degrees of freedom = -1<BR>\n" );
document.write( "area to the left = .181609\r<BR>\n" );
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document.write( "t-score with 50 degrees of freedom = -1<BR>\n" );
document.write( "area to the left = .161063\r<BR>\n" );
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document.write( "t-score with 1000 degrees of freedom = -1<BR>\n" );
document.write( "area to the left = .158776\r<BR>\n" );
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document.write( "as the degrees of freedom get greater, the area to the left of the t-score approaches the area to the left of the z-score.\r<BR>\n" );
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document.write( "the difference is most pronounced when the degrees of freedom are small.\r<BR>\n" );
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document.write( "here's a reference that shows you the difference between a t distribution and a z distribution.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/t-distribution.html#:~:text=What's%20the%20key%20difference%20between,on%20the%20sample%20standard%20deviation.\" target = \"_blank\">https://www.jmp.com/en_us/statistics-knowledge-portal/t-test/t-distribution.html#:~:text=What's%20the%20key%20difference%20between,on%20the%20sample%20standard%20deviation.</a> </SPAN>\n" );
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