document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201383>Question 1201383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The prime Minister of a small Caribbean Island stated that 95% of the population was vaccinated from the Covid-19 virus. The opposition believes that the Minister is overstating the proportion of vaccinated citizens. He randomly selects 300 citizens and found that 240 of them were fully vaccinated. \r<BR>\n" );
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document.write( "i. Calculate a 99% confidence interval for the true proportion of all citizens who were vaccinated.<BR>\n" );
document.write( "ii. Interpret you answer in i).<BR>\n" );
document.write( "iii. State the null and alternative hypothesis of this test.  <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 #835730 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=835730\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population is assumed to be 95% vaccinated equals a population ratio of .95.<BR>\n" );
document.write( "sample of 300 finds that 240 of them were fully vaccinated.<BR>\n" );
document.write( "sample has a ratio of 240 / 300 = .8<BR>\n" );
document.write( "standard error for the test is sqrt(.95 * .05 / 300) = .0125830574.<BR>\n" );
document.write( "the population ratio is used in the calculation of the standard error for the test.<BR>\n" );
document.write( "use the z-score formula to find the probability of getting a score less than .8.<BR>\n" );
document.write( "z = (x - m) / s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the sample ratio<BR>\n" );
document.write( "m is the population ratio<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "you get z = (.8 - .9) / .0125830574 = -7.947194142.<BR>\n" );
document.write( "the 99% confidence interval for the z-score would be plus or minus z = 2.575829303.<BR>\n" );
document.write( "since the absolute value of the test z-score is greater than tha absolute value of the critical z-score, the test is considered significant and the conclusion is that ratio is not .95, but something less than that.\r<BR>\n" );
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