document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=136488>Question 136488</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A coin was flipped 60 times and came up heads 38 times. (a) At the .10 level of significance, is the<BR>\n" );
document.write( "coin biased toward heads? Show your decision rule and calculations. (b) Calculate a p-value and<BR>\n" );
document.write( "interpret it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #99992 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=99992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A coin was flipped 60 times and came up heads 38 times. <BR>\n" );
document.write( "(a) At the .10 level of significance, is the coin biased toward heads? Show your decision rule and calculations.<BR>\n" );
document.write( "Ho: p=1/2<BR>\n" );
document.write( "Ha: p is not 1/2<BR>\n" );
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document.write( "p-hat = 38/60 = 0.63333...<BR>\n" );
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document.write( "Critical value for 2-tail z-test with alpha = 10%: z = +/- 1.645<BR>\n" );
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document.write( "Test statistic: <BR>\n" );
document.write( "z(0.633333) = (0.6333-0.5)/sqrt[(0.5)(0.5)/60] = 0.13333/0.064549..= 2.0656<BR>\n" );
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document.write( "(b) Calculate a p-value and interpret it.<BR>\n" );
document.write( "p-value = P(2.0656 < z < 10 ) = 2*0.019434..= 0.03887..<BR>\n" );
document.write( "Interpretation: Only 0.03887 of test results could have given<BR>\n" );
document.write( "stronger evidence for rejecting Ho.<BR>\n" );
document.write( "Conclusion: Since p-value < alpha, reject Ho.<BR>\n" );
document.write( "This is statistical evidence that the coin is biased.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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