document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1189975>Question 1189975</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.We wish to estimate what percent of 18 to 25-year old's that own a Samsung phone. Out of 400 sampled, 104 had a Samsung phone. Based on this, construct a 90% confidence interval for the proportion of all adults that own a Samsung phone.\r<BR>\n" );
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document.write( "2. A 2011 Gallup survey based on telephone and face-to-face interviews with a sample of adults in China suggests that 20% smoke regularly or occasionally, with a margin of error of 2.2%. Give the confidence interval.\r<BR>\n" );
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document.write( "3. You want to obtain a sample to estimate the average number of hours per week community college students in the United States work at their job while being a full-time student. Based on previous evidence, you believe the population standard deviation is 10. You would like to be 99% confident that your estimate is within 1.5 hours of the true population mean. <BR>\n" );
document.write( "Assume that the number of statistics students is unknown, but very large. How large of a sample size is required? \r<BR>\n" );
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document.write( "4.You want to obtain a sample to estimate the average number of hours per week Nexford students work at their job while being a full-time student. Based on previous evidence, you believe the population standard deviation is 10. You would like to be 99% confident that your estimate is within 1.5 hours of the true population mean.  <BR>\n" );
document.write( "Assume that the number of students at Nexford is 2900 students. How large of a sample size <BR>\n" );
document.write( "is required? \r<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 #821497 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "In the future, please only post one problem at a time.\r<BR>\n" );
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document.write( "I'll do problem 1 to get you started.\r<BR>\n" );
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document.write( "n = 400 = sample size<BR>\n" );
document.write( "x = 104 = number who have a Samsung phone<BR>\n" );
document.write( "phat = x/n = 104/400 = 0.26<BR>\n" );
document.write( "The sample proportion phat estimates the population proportion p.\r<BR>\n" );
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document.write( "At 90% confidence, the z critical value is roughly z = 1.645 (use a table or calculator to find this value).<BR>\n" );
document.write( "We can use the Z distribution because n > 30.\r<BR>\n" );
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document.write( "Let's calculate the lower and upper bounds of the confidence interval.\r<BR>\n" );
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document.write( "L = lower bound of confidence interval<BR>\n" );
document.write( "L = phat - z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "L = 0.26 - 1.645*sqrt(0.26*(1-0.26)/400)<BR>\n" );
document.write( "L = 0.26 - 0.03607766656811<BR>\n" );
document.write( "L = 0.26 - 0.036<BR>\n" );
document.write( "L = 0.224\r<BR>\n" );
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document.write( "U = upper bound of confidence interval<BR>\n" );
document.write( "U = phat + z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "U = 0.26 + 1.645*sqrt(0.26*(1-0.26)/400)<BR>\n" );
document.write( "U = 0.26 + 0.03607766656811<BR>\n" );
document.write( "U = 0.26 + 0.036<BR>\n" );
document.write( "U = 0.296\r<BR>\n" );
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document.write( "The confidence interval is in the format of (L, U)\r<BR>\n" );
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document.write( "Answer: <font color=red>(0.224, 0.296)</font><BR>\n" );
document.write( "We're 90% confident that the population proportion p is somewhere between 0.224 and 0.296<BR>\n" );
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