document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1003683>Question 1003683</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear tutor,<BR>\n" );
document.write( "I have a problem with CI section. Any help is appreciated. Thank you.\r<BR>\n" );
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document.write( "Q. You take a sample of 22 from a population of test scores, and the mean of your sample is 60. \r<BR>\n" );
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document.write( "(a) You know the standard deviation of the population is 10. What is the 99% confidence interval on the population mean. \r<BR>\n" );
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document.write( "I got standard error of the mean which is 10/ square root of 22 =2.13<BR>\n" );
document.write( "mean +- (Standard deviation of 99%)(2.13)= ??\r<BR>\n" );
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document.write( "If this formula is right how do I get standard deviation for 99%? I used normal distribution calculator the answer was between 34.2417 and 85.7583. It doesn't seem right. \r<BR>\n" );
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document.write( "(b) Now assume that you do not know the population standard deviation, but the standard deviation in your sample is 10. What is the 99% confidence interval on the mean now? \r<BR>\n" );
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document.write( "I still have standard error of the mean which is 2.13\r<BR>\n" );
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document.write( "I assume I use t table so I looked at 99% for df 21. the value was 2.831<BR>\n" );
document.write( "so I tried to put these number to the formula above but I can't because I don't know how to get SD of 99%. .04)<BR>\n" );
document.write( "The book says answer for (b) is (53.96, 6\r<BR>\n" );
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document.write( "Please help. thank you in advance. <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 #620428 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=620428\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To calculate a confidence interval we need the confidence level, statistic, and margin of error.<BR>\n" );
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document.write( "a) margin of error = critical value * standard deviation of statistic<BR>\n" );
document.write( "we want the 99% confidence interval on the population mean, <BR>\n" );
document.write( "note that we use the t-distribution because our sample size is < 30<BR>\n" );
document.write( "the degrees of freedom(df) = 22 - 1 = 21<BR>\n" );
document.write( "t(alpha/2) is determined by consulting the t-distribution table<BR>\n" );
document.write( "t(alpha/2) for 99% cf is 2.831<BR>\n" );
document.write( "99% cf for population mean = 60 + or - (t(alpha/2) * (10/sqrt(22)) =<BR>\n" );
document.write( "60 + or - (2.831 * 2.13) = 60 + or - 6.03<BR>\n" );
document.write( "our 99% cf is (53.97, 66.03)<BR>\n" );
document.write( "note that the sample mean is also the population mean<BR>\n" );
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document.write( "b) the std dev of the sample = st dev of population / sqrt(sample size)<BR>\n" );
document.write( "for this part of the problem<BR>\n" );
document.write( "std dev of the population = 10 * sqrt(22) = 46.9<BR>\n" );
document.write( "99% cf for population mean = 60 + or - 2.831 * (46.9/sqrt(22)) =<BR>\n" );
document.write( "60 + or - 28.3 = (31.7, 88.3)<BR>\n" );
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