document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1120622>Question 1120622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Tutor<BR>\n" );
document.write( "please help me with stats question\r<BR>\n" );
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document.write( "In a random sample of 200 observations,we found the proportion of successes to be 48%.<BR>\n" );
document.write( "Use a 90% degree of confidence to estimate the population proportion of successes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #736278 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=736278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in a proportion type problem:\r<BR>\n" );
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document.write( "p = the proportion of successes<BR>\n" );
document.write( "q = the proportion of failures = 1 minus the proportion of successes<BR>\n" );
document.write( "n = total number of observations = sample size\r<BR>\n" );
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document.write( "the formulas to use are:\r<BR>\n" );
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document.write( "p = .48 = proportion of successes<BR>\n" );
document.write( "q = 1 - .48 = .52 = proportion of failures\r<BR>\n" );
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document.write( "mean = p<BR>\n" );
document.write( "standard error = sqrt(p*q/n)<BR>\n" );
document.write( "z = (x-m)/s<BR>\n" );
document.write( "x = raw score<BR>\n" );
document.write( "m = raw mean<BR>\n" );
document.write( "s = standard error\r<BR>\n" );
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document.write( "90% degree of confidence results in a z-score of plus or minus 1.644853626 when using the TI-84 Plus scientific calculator.\r<BR>\n" );
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document.write( "90% confidence interval results in an alpha o\r<BR>\n" );
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document.write( "the alpha is the area under the normal distribution curve which is outside the confidence interval.\r<BR>\n" );
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document.write( "look for the z-score that has an area of .05 to the left of it gives you the negative critical z-score.\r<BR>\n" );
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document.write( "look for the z-score that has an area of .95 to the left of it gives you the positive critical z-score.\r<BR>\n" );
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document.write( "a z-score that has an area of.95 to the left of it is the same as a z-score that has an area of .05 to the right of it.\r<BR>\n" );
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document.write( "in your problem:\r<BR>\n" );
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document.write( "m is the mean which is equal to p which is equal to .48<BR>\n" );
document.write( "n is the sample size which is equal to 200\r<BR>\n" );
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document.write( "s is the standard error which is equal to sqrt(p*q/n) which is equal to sqrt(.48*.52/200) which is equal to .0353270435\r<BR>\n" );
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document.write( "critical low z-score is equal to -1.644853626 <BR>\n" );
document.write( "critical high z-score is equal to 1.644853626 \r<BR>\n" );
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document.write( "to find the low raw score, you use z=(x-m)/s which becomes -1.644853626  = (x-.48)/.0353270435.<BR>\n" );
document.write( "solve for x to get x = z*s+m which becomes x = -1.644853626 * .0353270435 + .48 which becomes x = .4218921845.\r<BR>\n" );
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document.write( "to find the high raw score, you use z=(x-m)/s which becomes 1.644853626 = ((x-.48)/.0353270435.<BR>\n" );
document.write( "solve for x to get x = 1*s+m which becomes x = 1.644853624 * .0353270435 + .48 which becomes x = .5381078155.\r<BR>\n" );
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document.write( "your 90% confident estimate of the population proportion is equal to anywhere between .4218921845 and .5381078155.\r<BR>\n" );
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document.write( "you would round as required.\r<BR>\n" );
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document.write( "visually this would look like the following.\r<BR>\n" );
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document.write( "first with z-scores\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/072903.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "next with raw scores\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/072903.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the area shown at the bottom of each display is your confidence level which is equal to .9 = 90%.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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