document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1184274>Question 1184274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An epidemiologist is worried about the ever increasing trend of malaria in a certain locality<BR>\n" );
document.write( "and wants to estimate the proportion of people infected in the peak malaria transmission<BR>\n" );
document.write( "period. If he takes a random sample of 150 people in that locality during the peak<BR>\n" );
document.write( "transmission period and finds that 60 of them are positive for malaria, find<BR>\n" );
document.write( "i. 99% confidence interval for the proportion of the whole infected people in that<BR>\n" );
document.write( "locality during the peak malaria transmission period.<BR>\n" );
document.write( "ii. Based on your results in part (i), do you think the epidemiologist’s worry is<BR>\n" );
document.write( "justified? Explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814814 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=814814\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 150<BR>\n" );
document.write( "60 are positive for malaria.<BR>\n" );
document.write( "the mean proportion is 60/150 = 6/15 = 2/5 = .4<BR>\n" );
document.write( "the mean proportion standard deviation is sqrt(.4 * .6) / 150) = .04<BR>\n" );
document.write( "critical z-score for 99% two-tailed confidence level is plus or minus 2.5758.\r<BR>\n" );
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document.write( "the z-score formula is z = (x - m) / s<BR>\n" );
document.write( "z is the z-score.<BR>\n" );
document.write( "x is the sample raw score proportion.<BR>\n" );
document.write( "m is the population mean proportion.<BR>\n" );
document.write( "s is the standard error = sqrt(p*q/n), where:<BR>\n" );
document.write( "p is the population proportion.<BR>\n" );
document.write( "q = 1 - p<BR>\n" );
document.write( "n is the sample size.\r<BR>\n" );
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document.write( "when z = -2.5758, the formula becomes:<BR>\n" );
document.write( "-2.5758 = (x - .4) / .04<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = -2.5758 * .04 + .4 = .297\r<BR>\n" );
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document.write( "when z = 2.5758, the formula becomes:<BR>\n" );
document.write( "2.5758 = (x - .4) / .04<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 2.5758 * .04 + .4 = .503.\r<BR>\n" );
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document.write( "i believe that's your two-tailed confidence interval.\r<BR>\n" );
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document.write( "with a sample size of 150, between 30% and 505 will show positive for malaria.\r<BR>\n" );
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document.write( "that a very high percentage, showing that the population is at high risk for malaria.\r<BR>\n" );
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document.write( "here's a world malaria report that shows where the highest risks are.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.gs.international/learning-centre-articles/malaria-world-map-risk\" target = \"_blank\">https://www.gs.international/learning-centre-articles/malaria-world-map-risk</a>\r<BR>\n" );
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document.write( "here's a reference on mean proportion and standard deviation.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Shafer_and_Zhang)/06%3A_Sampling_Distributions/6.03%3A_The_Sample_Proportion#:~:text=at%20least%2030.-,The%20Sampling%20Distribution%20of%20the%20Sample%20Proportion,interval%20%5B0%2C1%5D.\" target = \"_blank\">https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(Shafer_and_Zhang)/06%3A_Sampling_Distributions/6.03%3A_The_Sample_Proportion#:~:text=at%20least%2030.-,The%20Sampling%20Distribution%20of%20the%20Sample%20Proportion,interval%20%5B0%2C1%5D.</a>\r<BR>\n" );
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document.write( "i'm never 100% certain that i'm right with these types of problems, but i'm reasonably certain that what i gave you is accurate.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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