document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174838>Question 1174838</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A smartphone company is interested in comparing the quality of work at two of its factories. By randomly selecting samples of smartphones manufactured at each factory and testing their reliability, the company will be able to estimate the proportion of malfunctioning smartphones manufactured at each factory. Of particular interest is the difference between these proportions. Independent simple random samples from the two offices provide the following information:\r<BR>\n" );
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document.write( "Factory 1\r<BR>\n" );
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document.write( "Factory 2\r<BR>\n" );
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document.write( "n1 = 250\r<BR>\n" );
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document.write( "n2 = 300\r<BR>\n" );
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document.write( "Number of malfunctioning phones = 35\r<BR>\n" );
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document.write( "Number of malfunctioning phones = 27\r<BR>\n" );
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document.write( "a.       What is the point estimate of the difference between the two population proportions (p1  -  p2)?  2pts\r<BR>\n" );
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document.write( "b.      Develop a 95% confidence interval for the difference between the two population proportions (p1  -  p2). 7pts\r<BR>\n" );
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document.write( "c.       Develop a 90% confidence interval for the difference between the two population proportions (p1  -  p2). 7pts </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #801849 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=801849\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p1=35/250=0.14<BR>\n" );
document.write( "p2=27/300=0.09<BR>\n" );
document.write( "p1-p2 point estimate is 0.05<BR>\n" );
document.write( "std error is sqrt { (p hat*(1- phat)* (1/n1)+(1/n2)} p hat is pooled proportion or 62/550=0.1127<BR>\n" );
document.write( "=sqrt ((p1*(1-p1)/n1+p2(1-p2)/n2))=sqrt(0.14*0.86/250+0.09*0.91/300)=0.0275<BR>\n" );
document.write( "multiply that by 1.96 to get the half-interval of the difference at the 95% level=0.0538\r<BR>\n" );
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document.write( "CI=(-0.0038, 0.1038)\r<BR>\n" );
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document.write( "for 90%, use 1.645 and get a half-interval of 0.0452<BR>\n" );
document.write( "CI=(0.0048, 0.0952)\r<BR>\n" );
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document.write( "Notice the first contains 0, so the p-value is between 0.05 and 0.10\r<BR>\n" );
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document.write( " </SPAN>\n" );
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