document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1182597>Question 1182597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ESTIMATING THE POPULATION MEAN WITH UNKNOWN VARIANCE USING A SMALL SAMPLE\r<BR>\n" );
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document.write( "The mean length 𝜇 of time consumed in online classes per day of Senior High School students would have to be estimated. A sample of 20 students had a mean of 3.5 hours a day with a sample standard deviation of 0.8 hour. Find the 95 % confidence interval for the 𝜇.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813634 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=813634\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sample mean is equal to 3.5 hours.<BR>\n" );
document.write( "the sample standard deviation is equal to .8 hours.<BR>\n" );
document.write( "the sample size is 20.\r<BR>\n" );
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document.write( "t-score would be used with 19 degrees of freedom is what i think.<BR>\n" );
document.write( "at 95% confidence level, the two tail critical t-score with 19 degrees of freedom would be equal to plus or minus 2.093.\r<BR>\n" );
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document.write( "19 degrees of freedom is because the sample size is 20.\r<BR>\n" );
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document.write( "the standard error would be equal to .8 / sqrt(20) = .1789.<BR>\n" );
document.write( "that's the standard deviation of the sample divided by the square root of the sample size.\r<BR>\n" );
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document.write( "the t-score formula becomes plus or minus 2.093 =  ​(x - 3.5) / .1789\r<BR>\n" );
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document.write( "solve for x to get:\r<BR>\n" );
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document.write( "x = .1789 * 2.093 + 3.5 on the high side and x = .1789 * -2.093 + 3.5 on the low side.\r<BR>\n" );
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document.write( "x will be equal to 3.8744377 on the high side.<BR>\n" );
document.write( "x will be equal to 3.1255623 on the low side.\r<BR>\n" );
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document.write( "your confidence interval is from 3.1256 on the low side to 3.8744 on the high side when the solution is rounded to 4 decimal places.\r<BR>\n" );
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document.write( "the graph of the critical t-score would look like this:\r<BR>\n" );
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document.write( "you need to find the standard error and use the t-score formula to find the raw scores from the t-scores.\r<BR>\n" );
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document.write( "i did that above.\r<BR>\n" );
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document.write( "standard error = standard deviation of sample divided by square root of sample size.\r<BR>\n" );
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document.write( "t-score formula is t = (x = m) / s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standard error\r<BR>\n" );
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document.write( " </SPAN>\n" );
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