document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974790>Question 974790</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the past, 20% of all airline passengers &#64258;ew &#64257;rst class. In a sample of 15 passengers, 5 &#64258;ew &#64257;rst class. At &#945; = 0.10, can you conclude that the proportions have changed? \r<BR>\n" );
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document.write( "Since sample size is less than 30, so T-test would be used. However, there is no Std Deviation and Sample Mean or 5 is actually the sample mean? I am not sure how to proceed.<BR>\n" );
document.write( "H0: p= 0.2, H1: p&#8800;0.2, <BR>\n" );
document.write( "T-test: x&#773;  - &#956; / (s/ sqrt n)<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 #596617 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=596617\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem is solved using \"Sample Distribution of the Proportion\"<BR>\n" );
document.write( "Use 2-tailed test and the following hypothesis:\r<BR>\n" );
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document.write( "Ho:  p1 = p2<BR>\n" );
document.write( "H1:  p1 not = p2\r<BR>\n" );
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document.write( "p1 = 0.20 and p2 is determined from the binomial distribution since a passenger is either first class or not\r<BR>\n" );
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document.write( "p2 = C(n,r) * p1^r * (1-p1)^n-r<BR>\n" );
document.write( "p2 = (15! / (5! * (15-5)!)) * (0.20)^5 * (1-0.20)^(15-5)<BR>\n" );
document.write( "p2 = ((15*14*13*12*11) / (5*4*3*2*1)) * 0.00032 * 0.107374182<BR>\n" );
document.write( "p2 = 3003 * 0.00032 * 0.107374182 = 0.103182294 approx 0.10\r<BR>\n" );
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document.write( "p2 is the sample mean and<BR>\n" );
document.write( "sample standard deviation is sqrt(pq/n) = sqrt((0.10*0.90)/15) = 0.077459667\r<BR>\n" );
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document.write( "now we want to compare p1 and p2 at alpha = 0.10 (using 2-tailed we have 0.05)\r<BR>\n" );
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document.write( "t = (0.20 - 0.10) / (0.077459667 / square root(15)) = 5<BR>\n" );
document.write( "now t14 for 0.05 is 2.145\r<BR>\n" );
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document.write( "Since the test stat is greater than the critical value, we reject the<BR>\n" );
document.write( "null at .05 two-tailed significance level<BR>\n" );
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