document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108899>Question 1108899</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that you wish to obtain a 95% confidence interval for a population mean. The population is normally distributed, the sample size is 20, and the population standard deviation is unknown. The correct procedure to use is the t-interval procedure.\r<BR>\n" );
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document.write( "(a)If you mistakenly use the z-interval procedure, will the resulting confidence interval be too wide or too narrow? Why?\r<BR>\n" );
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document.write( "(b)Will the true confidence level associated with this interval be greater than or less than 95%?<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 #724147 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=724147\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 20.\r<BR>\n" );
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document.write( "z-score for 95% confidence interval would be plus or minus 1.959963986.\r<BR>\n" );
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document.write( "t-score for 95% confidence interval would be plus or minus 2.093024022, using 19 degrees of freedom (sample size of 20 - 1 = 19 degrees of freedom).\r<BR>\n" );
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document.write( "if you mis-understood the z-score to be the t-score, the resulting confidence interval would be too narrow.\r<BR>\n" );
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document.write( "if the z-score was interpreted as the t-score, then a t-score of plus or minus 1.959963986 with 19 degrees of freedom would generate a confidence level of .9351665248 = 93.5%.\r<BR>\n" );
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document.write( "that would be less than the desired 95%.\r<BR>\n" );
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