document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129929>Question 129929</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Recently the national average yield on municipal bonds has been &#956; = 4.19%.  A random sample of 16 Arizona municipal bonds gave an average yield of 5.11% with a sample standard deviation s = 1.15%.  Does this indicate that the population mean yield for all Arizona municipal bonds is greater than the national average?  Use &#945; = 0.05.  Assume x is normally distributed.\r<BR>\n" );
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document.write( "a) State the null and the alternate hypothesis.<BR>\n" );
document.write( "b) Identify the sampling distribution to be used:  the standard normal distribution or the Student's t distribution. Find the critical value(s).<BR>\n" );
document.write( "c) Compute the z or t value of the sample test statistic.<BR>\n" );
document.write( "d) Find the P value or an interval containing the P value for the sample test statistic.<BR>\n" );
document.write( "e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level.  Explain your conclusion in the context of the 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 #94959 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=94959\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Recently the national average yield on municipal bonds has been &#956; = 4.19%. A random sample of 16 Arizona municipal bonds gave an average yield of 5.11% with a sample standard deviation s = 1.15%. Does this indicate that the population mean yield for all Arizona municipal bonds is greater than the national average? Use &#945; = 0.05. Assume x is normally distributed. <BR>\n" );
document.write( "a) State the null and the alternate hypothesis.<BR>\n" );
document.write( "Ho: mu = 0.0419<BR>\n" );
document.write( "Ha: mu > 0.0419<BR>\n" );
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document.write( "b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution.<BR>\n" );
document.write( "Ans: t-distribution because we are testing the population mean value.<BR>\n" );
document.write( "Find the critical value(s).<BR>\n" );
document.write( "One-tail test with alpha=5% and 15 df ; critical value: t =1.753<BR>\n" );
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document.write( "c) Compute the z or t value of the sample test statistic.<BR>\n" );
document.write( "t(5.11) = (0.0511- 0.0419)<BR>\n" );
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document.write( "d) Find the P value or an interval containing the P value for the sample test statistic.<BR>\n" );
document.write( "p-value = P(0.0419 <= t < 10 with 15 df) = 0.4836...<BR>\n" );
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document.write( "e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level.<BR>\n" );
document.write( "Since the p-value is greater than alpha, fail to reject Ho.<BR>\n" );
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document.write( " Explain your conclusion in the context of the problem.<BR>\n" );
document.write( "There is strong statistical evidence that we should not reject<BR>\n" );
document.write( "the claim that mu = 4.19%<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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