document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=436310>Question 436310</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A battery operated digital pressure monitor is being developed for use in calibrating pneumatic pressure gauges in the field. It is thought that 95% of the readings it gives lie within 0.01 lb/in^2 of the true reading. In a series of 100 tests, the gauge is subjected to a pressure of 10,000 lb/in^2. A test is considered to be a success if the reading lies withing 10,000 +/- lb/in^2. We want to tst Ho: p=.95 H1: p does not equal .95 at the alpha = .05 level.\r<BR>\n" );
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document.write( "A. What are the critical points for the test?\r<BR>\n" );
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document.write( "B. When the data are gathered, it is found that 98 of the 100 readings were successful. Can Ho be rejected at the alpha =.05 level? To what type error are you now subject?\r<BR>\n" );
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document.write( "THANK YOU in advance.<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 #301874 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=301874\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A battery operated digital pressure monitor is being developed for use in calibrating pneumatic pressure gauges in the field. <BR>\n" );
document.write( "It is thought that 95% of the readings it gives lie within 0.01 lb/in^2 of the true reading. <BR>\n" );
document.write( "In a series of 100 tests, the gauge is subjected to a pressure of 10,000 lb/in^2. A test is considered to be a success if the reading lies withing 10,000 +/- (?)lb/in^2. We want to test <BR>\n" );
document.write( "Ho: p=.95 <BR>\n" );
document.write( "H1: p does not equal .95<BR>\n" );
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document.write( "at the alpha = .05 level. <BR>\n" );
document.write( "A. What are the critical points for the test?<BR>\n" );
document.write( "z = +/-1.96<BR>\n" );
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document.write( "B. When the data are gathered, it is found that 98 of the 100 readings were successful. Can Ho be rejected at the alpha =.05 level?<BR>\n" );
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document.write( "z(0.98) = (0.98-0.95)/sqrt[0.95*0.05/100] = 1.3765<BR>\n" );
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document.write( "Since the test stat is not in the reject interval,<BR>\n" );
document.write( "fail to reject Ho.<BR>\n" );
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document.write( "By the way, the p-value = 2*P(z> 1.3765) = 2*0.0843 = 0.1686<BR>\n" );
document.write( "Since the p-value is greater than 5% fail to reject Ho.<BR>\n" );
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document.write( "To what type error are you now subject? <BR>\n" );
document.write( "Ans: You have not reject Ho.  You are subject<BR>\n" );
document.write( "to a Type II error.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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