document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1051026>Question 1051026</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could someone please help with this?:\r<BR>\n" );
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document.write( "The SAT math scores for all seniors in a high school are normally distributed with population standard deviation of 200.  100 seniors from the school are randomly selected, and their SAT math scores has a sample mean of 650.\r<BR>\n" );
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document.write( "(a) What distribution will you use to determine the critical value for a confidence interval estimate of the mean SAT math score for the seniors in the high school? Why?\r<BR>\n" );
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document.write( "(b) Construct a 95% confidence interval estimate of the mean SAT math score for the seniors in the high school. (Show work and round the answer to two decimal places)\r<BR>\n" );
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document.write( "(c) Is a 90% confidence interval estimate of the mean SAT math score wider than the 95% confidence interval estimate you got from part (b)? Why? [You don’t have to construct the 90% confidence interval]\r<BR>\n" );
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document.write( "Thank you for any help!<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 #666645 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=666645\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The SAT math scores for all seniors in a high school are normally distributed<BR>\n" );
document.write( " with population standard deviation of 200. <BR>\n" );
document.write( "n = 100,  x&#772; = 650<BR>\n" );
document.write( "(a)<BR>\n" );
document.write( "Find a 95% confidence interval estimate of The mean SAT math score for HS seniors\r<BR>\n" );
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document.write( "Population SD Known:  will use a z score analysis:<BR>\n" );
document.write( " z = invNorm((1-.95)/2) = invNorm(.05)<BR>\n" );
document.write( "critical value equal to z = 1.96\r<BR>\n" );
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document.write( "(b )<BR>\n" );
document.write( "ME =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+z%2Asigma%2Fsqrt%28n%29 ALIGN=MIDDLE  ALT=\"+z%2Asigma%2Fsqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "ME = 1.96(200/10) = 39.2<BR>\n" );
document.write( "650 ± 39.2<BR>\n" );
document.write( "We are 95% confident that the mean SAT math score for the seniors is:<BR>\n" );
document.write( "between 614.8 and 689.2<BR>\n" );
document.write( "Check Arithmetic<BR>\n" );
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document.write( "(c) Is a 90% confidence interval estimate of the mean SAT math score wider <BR>\n" );
document.write( "than the 95% confidence interval estimate you got from part (b)? NO<BR>\n" );
document.write( "Why? 90% confidence interval z = 1.645 (which is <1.96 Multiplying by smaller number)<BR>\n" );
document.write( "Less accuracy, smaller interval<BR>\n" );
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