document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=663663>Question 663663</A>: <I><SPAN STYLE=\"word-break: break-all;\"> These problems I have been working on all weekend, and I do not understand. My grade and passing the course depends on this. HOWEVER, I have not received a single reply. WHY?  Very unusual, from the tutors here! I need your help, if I could pay I would! It is that important.<BR>\n" );
document.write( "Problem 1: Assume that the mean score on a certain aptitude test across the nation is 100,and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is 100. (Points:3)<BR>\n" );
document.write( "Solution what I am doing right or wrong: z=(100)=(100-100)/20=-0/20=<BR>\n" );
document.write( "Problem2:.Assume that a sample is drawn and z(a/2) =1.96 and &#963;=35. Answer the following questions:<BR>\n" );
document.write( "	If the Maximum Error of Estimate is 0.02 for this sample, what would be the sample size? ( I got this far: N=zs/E)^2N= (1.96 *35/)(.02^2=) don’t know if I am doing it right)<BR>\n" );
document.write( "	Given that the sample SIZE is 400 with this same z(a/2) and &#963;, what would be the Maximum  Error of Estimate? (My workings are E= zs/sqrt(n) E= 1.96*35/sqrt400=.606)<BR>\n" );
document.write( "	What happens to the Maximum Error of Estimate as the sample size gets smaller? (I have no idea)<BR>\n" );
document.write( "	 What effect does the answer to C above have to the size of the confidence interval? (My work; As sample gets larger the ME gets smaller so the CI gets smaller.) (Points:8)<BR>\n" );
document.write( "Problem:3 By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the SD is 4.34 seconds. Answer all of the question by showing your work:<BR>\n" );
document.write( "	How many measurements should be made in order to be 90% CERTAIN that the ME of estimation will not exceed 2.0 seconds?<BR>\n" );
document.write( "	What sample size is required for a ME of 0.5 seconds? (Points:6) <BR>\n" );
document.write( "(My work: a) 1-a=0.90 =2.0 ) TOTALLY LOST<BR>\n" );
document.write( "Problem 3: A 99% confidence interval estimate for a population mean was computed to be (47.1, 65.9). Determine the mean of the sample, which was used to determine the interval <BR>\n" );
document.write( "                Estimate. (Must show all work) Points: 4)  ( z=0.4761  0.6591) from table 3- I really don’t know) just guessing … <BR>\n" );
document.write( "Problem:4: A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having 2 children. A sample of 185 was taken, and the mean amount spent was $244.16. Assuming a SD equal to $38.98, find the 98% confidence interval for &#956;, the mean for all such families. (Show ALL work) (Points 4).  (Don’t know where to start as I am very confused)\r<BR>\n" );
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document.write( "Please answer me this time around.... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412877 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=412877\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Problem 1: Assume that the mean score on a certain aptitude test across the nation is 100,and that the standard deviation is 20 points. Find the probability that the mean aptitude test score for a randomly selected group of 150 8th graders is 100. (Points:3)<BR>\n" );
document.write( "Solution what I am doing right or wrong: z=(100)=(100-100)/20=-0/20=0<BR>\n" );
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document.write( "Note: In a continuous distribution the probability of gettin ANY exact<BR>\n" );
document.write( "score is zero.<BR>\n" );
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document.write( "Problem2:.Assume that a sample is drawn and z(a/2) =1.96 and &#963;=35. Answer the following questions:<BR>\n" );
document.write( "If the Maximum Error of Estimate is 0.02 for this sample, what would be the sample size? ( I got this far: <BR>\n" );
document.write( "N = (zs/E)^2<BR>\n" );
document.write( "N = (1.96 *35/0.02)^2<BR>\n" );
document.write( "=  11,764,900<BR>\n" );
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document.write( "Given that the sample SIZE is 400 with this same z(a/2) and &#963;, what would be the Maximum Error of Estimate? <BR>\n" );
document.write( "E= zs/sqrt(n)<BR>\n" );
document.write( "E= 1.96*35/sqrt(400) = 3.43<BR>\n" );
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document.write( "What happens to the Maximum Error of Estimate as the sample size gets smaller? <BR>\n" );
document.write( "E = z*s/sqrt(n)<BR>\n" );
document.write( "Notice that E and sqrt(n) are indirectly related.<BR>\n" );
document.write( "So, as n gets smaller, E must get larger.<BR>\n" );
document.write( "Try it with numbers and you will see what I mean.<BR>\n" );
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document.write( "What effect does the answer to C above have to the size of the confidence interval? (My work; As sample gets larger the ME gets smaller so the CI gets smaller.) (Points:8)<BR>\n" );
document.write( "Correct<BR>\n" );
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document.write( "Problem:3 By measuring the amount of time it takes a component of a product to move from one workstation to the next, an engineer has estimated that the SD is 4.34 seconds. Answer all of the question by showing your work:<BR>\n" );
document.write( "How many measurements should be made in order to be 90% CERTAIN that the ME of estimation will not exceed 2.0 seconds?<BR>\n" );
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document.write( "n = [z*s/E]^2 = [1.645*4.34/2]^2 = 13 when rounded up<BR>\n" );
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document.write( "What sample size is required for a ME of 0.5 seconds? (Points:6) <BR>\n" );
document.write( "Same formula with 0.5 replacing 2.<BR>\n" );
document.write( "Ans: 204 when rounded up<BR>\n" );
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document.write( "Problem 3: A 99% confidence interval estimate for a population mean was computed to be (47.1, 65.9). Determine the mean of the sample, which was used to determine the interval Estimate.<BR>\n" );
document.write( "Note: The width of the CI is ALWAYS 2*ME<BR>\n" );
document.write( "2*ME = 65.9-47.1 = 18.8<BR>\n" );
document.write( "ME = 9.4<BR>\n" );
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document.write( "Note The sum of the CI limits is ALWAYS 2*(sample mean)<BR>\n" );
document.write( "2(sample mean) = 65.9+47.1 = 113<BR>\n" );
document.write( "sample mean = 56.5<BR>\n" );
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document.write( " <BR>\n" );
document.write( "Problem:4: A study was conducted to estimate the mean amount spent on birthday gifts for a typical family having 2 children. A sample of 185 was taken, and the mean amount spent was $244.16. Assuming a SD equal to $38.98, find the 98% confidence interval for &#956;, the mean for all such families. (Show ALL work) (Points 4). (Don’t know where to start as I am very confused)<BR>\n" );
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document.write( "x-bar = 244.16<BR>\n" );
document.write( "ME = 2.3263*38.98/sqrt(185) = 6.67<BR>\n" );
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document.write( "98% CI: 244.16-6.67 < u < 244.16+6.67<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. \r<BR>\n" );
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