document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198771>Question 1198771</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of 150 college students regarding their work schedules produce a<BR>\n" );
document.write( "mean of 25.4 hours worked per week with a standard deviation of 12 hours.<BR>\n" );
document.write( "a) What is the point estimate of mean time worked per week? Calculate margin of<BR>\n" );
document.write( "error when α = 0.01.<BR>\n" );
document.write( "b) Construct a 95% confidence interval for the mean number of hours worked per week<BR>\n" );
document.write( "by college students </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833180 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=833180\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) What is the point estimate of mean time worked per week? Calculate margin of<BR>\n" );
document.write( "error when α = 0.01.\r<BR>\n" );
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document.write( "the point estimate of the mean time worked per week is the mean of the sample which is equal to 25.4 hours worked per week.\r<BR>\n" );
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document.write( "the margin of error when alpha = .01 is found by using the t-score as follows:<BR>\n" );
document.write( "note that you are using the t-score rather than the z-score because the standard deviation is taken from the sample rather than from the population.<BR>\n" );
document.write( "t-score formula is:<BR>\n" );
document.write( "t = (x-m)/s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error<BR>\n" );
document.write( "standard error = standard deviation / square root of sample size = 12/sqrt(150) = .9797958971.<BR>\n" );
document.write( "at two sided alpha of .01, the alpha on each side will be .01/2 = .005<BR>\n" );
document.write( "at 149 degrees of freedom, the critical t-score will be plus or minus plus or minus 2.609227895.<BR>\n" );
document.write( "use the plus value in the t-score formula to find the margin of error.<BR>\n" );
document.write( "you will get:<BR>\n" );
document.write( "2.609227895 = (x - 25.4) / .9797958971.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 2.609227895 * .9797958971 + 25.4 = 27.95651079.<BR>\n" );
document.write( "subtract 25.4 from that to get margin of error = 2.556510786.<BR>\n" );
document.write( "that's your margin of error.\r<BR>\n" );
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document.write( "b) Construct a 95% confidence interval for the mean number of hours worked per week by college students.\r<BR>\n" );
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document.write( "95% confidence interval will have an alpha tail on each end equal to .05/2 = .025.<BR>\n" );
document.write( "the critical t-score with 149 degrees of freedom will be plus or minus plus or minus 1.976013145.<BR>\n" );
document.write( "when t = 1.976013145, t-score formula becomes 1.976013145 = (x - 25.4) / .9797958971.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 1.976013145 * 1.976013145 + 25.4 = 27.33608957.<BR>\n" );
document.write( "when t = -1.976013145, t-score formula becomes -1.976013145 = (x - 25.4) / .9797958971.<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = -1.976013145 * 1.976013145 + 25.4 = 23.46391043.<BR>\n" );
document.write( "your 95% confidence interval is from 23.46391043 to 27.33608957.\r<BR>\n" );
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document.write( "i've checked this a few times and i'm pretty sure this is correct.<BR>\n" );
document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo </SPAN>\n" );
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