document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1156490>Question 1156490</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A survey of 53 randomly selected \"iPhone\" owners showed that the purchase price  has a mean of $412 with a sample standard deviation of $180.<BR>\n" );
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document.write( "a.	Compute the standard error of the sample mean. (Round the final answer to the nearest whole number.)<BR>\n" );
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document.write( "  Standard error	 \r<BR>\n" );
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document.write( "b.	Compute the 80% confidence interval for the mean. (Round the final answers to 2 decimal places.)<BR>\n" );
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document.write( "  The confidence interval is between <BR>\n" );
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document.write( "c.	How large a sample is needed to estimate the population mean within $14 at a 80% degree of confidence? (Round the final answer to the nearest whole number.)<BR>\n" );
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document.write( "  Sample size	 <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 #779260 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=779260\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the t value (0.90) is +/-1.298<BR>\n" );
document.write( "SE is s/sqrt(n)=180/sqrt(53)=24.72 or 25<BR>\n" );
document.write( "80%CI is t*SE=depends on how it is rounded.  If I round only at the end, then it is 32.09<BR>\n" );
document.write( "that is on either side of mean 412<BR>\n" );
document.write( "(379.91, 444.09) $ units\r<BR>\n" );
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document.write( "$14=1.28*180/sqrt(n).  Because I don't know the sample size, I don't know t, but I can use z to approximate.<BR>\n" );
document.write( "square both sides<BR>\n" );
document.write( "196=53084/n<BR>\n" );
document.write( "n=270.84 or 271.  At this point, use the t value for that which make the interval a little wider, so then use the next higher and the next higher.<BR>\n" );
document.write( "n=273 gives ($398, $412)\r<BR>\n" );
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