document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182685>Question 1182685</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value tα/2​, ​(b) find the critical value zα/2​, or​ (c) state that neither the normal distribution nor the t distribution applies.\r<BR>\n" );
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document.write( "Here are summary statistics for randomly selected weights of newborn​ girls: n = 187​, x̄ = 28.1 ​hg, s = 6.1 hg. The confidence level is 95​%.\r<BR>\n" );
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document.write( "Select the correct choice below​ and, if​ necessary, fill in the blank to complete your choice.\r<BR>\n" );
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document.write( "A. tα/2 = __<BR>\n" );
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document.write( "B. zα/2 = __<BR>\n" );
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document.write( "C. Neither the normal distribution nor the t distribution applies. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #812822 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=812822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It is a relatively large sample size, and if one believes in the rule of 30 regardless, a z-test would be used. However, I prefer using a t-test since the sd used is from the sample. The difference is <1% with a sample size this large.  While the population weight is skewed somewhat, it is not likely to such a degree that a random sample of 187 could not be construed to be normally distributed. <BR>\n" );
document.write( "t(alpha/2)=1.97<BR>\n" );
document.write( "z(alpha/2)=1.96<BR>\n" );
document.write( "If you've not studied the rule of 30 for sample size, use t.<BR>\n" );
document.write( "If you were taught the rule of 30 means you can use z, use it.<BR>\n" );
document.write( "But notice the small difference between the two with this sample size. </SPAN>\n" );
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