document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=523155>Question 523155</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent. Of 200 children sampled, 123 rated it excellent. Using the .10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flaŽvor excellent? \r<BR>\n" );
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document.write( "(a) State the null hypothesis and the alternate hypothesis.<BR>\n" );
document.write( "(b) What is the probability of a Type I error?<BR>\n" );
document.write( "(c) Is this a one-tailed or a two-tailed test?<BR>\n" );
document.write( "(d) What is the decision rule?<BR>\n" );
document.write( "(e) What is the value of the test statistic?<BR>\n" );
document.write( "(f) What is your decision regarding the null hypothesis?<BR>\n" );
document.write( "(g) What is the p-value? Explain what it means in terms of this problem.<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 #347189 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=347189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Of 150 adults who tried a new rum-flavored peppermint patty, 87 rated it excellent.:: pa-hat = 87/150 = 0.580 <BR>\n" );
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document.write( "Of 200 children sampled, 123 rated it excellent.:: pc=hat = 123/200 = 0.615<BR>\n" );
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document.write( "Using the .10 level of significance, can we conclude that there is a significant difference in the proportion of adults and the proportion of children who rate the new flaŽvor excellent?<BR>\n" );
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document.write( "(a) State the null hypothesis and the alternate hypothesis.<BR>\n" );
document.write( "Ho: pa-pc = 0<BR>\n" );
document.write( "Ha: pa-pc is not 0<BR>\n" );
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document.write( "(b) What is the probability of a Type I error?::P(Type I) = alpha = 10%<BR>\n" );
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document.write( "(c) Is this a one-tailed or a two-tailed test?:::: 2-tail<BR>\n" );
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document.write( "(d) What is the decision rule?:: Reject Ho is test stat <-1.645 or >+1.645<BR>\n" );
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document.write( "(e) What is the value of the test statistic?:::<BR>\n" );
document.write( "ts = (0.580-0.615)/sqrt[(.58*0.42/150)+(0.615*0.385/200)] = -0.6605<BR>\n" );
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document.write( "(f) What is your decision regarding the null hypothesis?<BR>\n" );
document.write( "Since the ts is not in a reject interval, fail to reject Ho.<BR>\n" );
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document.write( "(g) What is the p-value? Explain what it means in terms of this problem.<BR>\n" );
document.write( "p-valu = 2*P(z < -0.6605) = 2*0.25 = 0.50<BR>\n" );
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document.write( "There is a 50% probability that the test results could have provided<BR>\n" );
document.write( "stronger evidence for rejecting Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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