document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163236>Question 1163236</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In order to conduct a hypothesis test for the population proportion, you sample 290 observations that result in 87 successes. (You may find it useful to reference the appropriate table: z table or t table)\r<BR>\n" );
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document.write( "H0: p ≥ 0.36; HA: p < 0.36.\r<BR>\n" );
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document.write( "1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)\r<BR>\n" );
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document.write( "2. Find the p-value.\r<BR>\n" );
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document.write( "  A. p-value > or equal to 0.10<BR>\n" );
document.write( "  B. p-value < 0.01<BR>\n" );
document.write( "  C. 0.01 < or equal to p-value < 0.025<BR>\n" );
document.write( "  D. 0.025 < or equal to p-value < 0.05<BR>\n" );
document.write( "  E. 0.05 < or equal to p-value < 0.10\r<BR>\n" );
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document.write( "3. At the 0.01 significance level, What is the conclusion?\r<BR>\n" );
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document.write( "  A.  Do not reject H0 since the p-value is smaller than significance level.<BR>\n" );
document.write( "  B.  Do not reject H0 since the p-value is greater than significance level.<BR>\n" );
document.write( "  C.  Reject H0 since the p-value is smaller than significance level.<BR>\n" );
document.write( "  D.  Reject H0 since the p-value is greater than significance level.\r<BR>\n" );
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document.write( "4. Interpret the results at α = 0.01\r<BR>\n" );
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document.write( "  A. We cannot conclude that the population mean is less than 0.36.<BR>\n" );
document.write( "  B. We conclude that the population mean is less than 0.36.<BR>\n" );
document.write( "  C. We cannot conclude that the population proportion is less than 0.36.<BR>\n" );
document.write( "  D. We conclude that the population proportion is less than 0.36. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788253 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=788253\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> z=(p hat-p)/sqrt((0.36*0.64)/290)<BR>\n" );
document.write( "=-0.06/0.0282=-2.13<BR>\n" );
document.write( "p-value is 0.0166\r<BR>\n" );
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document.write( "Answer to 2 is C<BR>\n" );
document.write( "Answer to 3 is B<BR>\n" );
document.write( "Answer to 4 is C. This is a population proportion, not a mean, and at the 0.01 level, we fail to reject the null hypothesis, so there is insufficient evidence to conclude that the population proportion is < 0.36.<BR>\n" );
document.write( "The p-value has to be less than the significance level, since the p-value says what the probability would be of finding a result this extreme or more, and that probability has to be lower than the postulated significance. </SPAN>\n" );
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