document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1065358>Question 1065358</A>: <I><SPAN STYLE=\"word-break: break-all;\"> #1 \r<BR>\n" );
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document.write( "You want to determine a confidence interval with a confidence level of 95%<BR>\n" );
document.write( "And 99% for the proportion of housewives who buy only once a week. <BR>\n" );
document.write( "If known<BR>\n" );
document.write( "That in a simple random sample of 400 housewives only 180 of said to buy one<BR>\n" );
document.write( "Once a week.\r<BR>\n" );
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document.write( "#2\r<BR>\n" );
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document.write( "A sample of 25 students from a Faculty has been obtained to estimate the<BR>\n" );
document.write( "Average grade of student records in the Faculty. It is known by other courses.<BR>\n" );
document.write( "That the standard deviation of the scores in said Faculty is of 2.01 points. If the average Of the sample was 4.9. Calculates:\r<BR>\n" );
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document.write( "1. Confidence interval at 90%.<BR>\n" );
document.write( "2. 95% Confidence Interval<BR>\n" );
document.write( "3. Confidence interval at 99%\r<BR>\n" );
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document.write( "#3\r<BR>\n" );
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document.write( "We want to obtain a confidence interval for the value of average sales<BR>\n" );
document.write( "Per hour that occur in a kiosk. For this, we perform a sample consisting of choosing At random the sales that were made during 1000 different hours; Shows whose results<BR>\n" );
document.write( "Were: average sales per hour 4000 pesos, and a standard deviation of 63,245 pesos. Get Said interval with a confidence level of 95%.\r<BR>\n" );
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document.write( "#4\r<BR>\n" );
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document.write( "The average height of a random sample of 400 people from a City is 1.75 m. It is known that the height of the people of that city is a aleatory variable  that follows a normal distribution with variance &#963;2 = 0.16 m2.\r<BR>\n" );
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document.write( "(A) Constructs an interval of 95% confidence for the mean of the height of the population.\r<BR>\n" );
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document.write( "(B) What would be the minimum sample size necessary to be able to be said to<BR>\n" );
document.write( "be True height of the statures is less than 2 cm from the sample mean, with a 90% confidence level?<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 #680519 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=680519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. One sample proportion, p=0.45, 1-p=0.55<BR>\n" );
document.write( "interval width for 95% is z(0.975)* sqrt ((p*(1-p))/n)=1.96* sqrt (0.2475/400)=0.0249*1.96=0.0488<BR>\n" );
document.write( "(0.4012, 0.4988).<BR>\n" );
document.write( "For 99%, z=2.576 and interval width is 0.0641 for (0.3859, 0.5141)<BR>\n" );
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document.write( "2. The 95% CI is x bar +/- t (df=24, 0.975)*2.01/sqrt (25)<BR>\n" );
document.write( "interval width is 2.064*2.01/5=0.83<BR>\n" );
document.write( "95% interval is (4.07, 5.73)<BR>\n" );
document.write( "90% interval uses 1.711 for t and has interval width of 0.70; (4.2, 5.6)<BR>\n" );
document.write( "99% interval uses 2.797 for t and has interval width of 1.12; (3.78, 6.02)<BR>\n" );
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document.write( "3. This doesn't appear to work with mean of 4000 and sd of 63,245; if such an sd is in fact the case, the distribution is not normal and can't use that. I think the 63.245 would likely be too small a sd.<BR>\n" );
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document.write( "4.Mean is 1.75 m and sigma is 0.4 m (sqrt of 0.16 m^2)<BR>\n" );
document.write( "95% CI interval width is is 1.96*0.4/20=0.0392<BR>\n" );
document.write( "(1.71, 1.79)<BR>\n" );
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document.write( "Need an interval width of 2 with z=1.645, sd 0.4 and n unknown<BR>\n" );
document.write( "2=1.645*0.4/ sqrt (n)<BR>\n" );
document.write( "sqrt (n)=1.645*0.4/0.02=32.9<BR>\n" );
document.write( "square both sides, and n=1082.41=1083. </SPAN>\n" );
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