document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=980611>Question 980611</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a simple random sample has been selected from a normally distributed population and test the given claim.<BR>\n" );
document.write( "Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test<BR>\n" );
document.write( "statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the<BR>\n" );
document.write( "original claim.<BR>\n" );
document.write( "Use a significance level of &#1049477; = 0.05 to test the claim that &#956; = 32.6. The sample data consist of<BR>\n" );
document.write( "15 scores for which x = 42.5 and s = 5.9. Use the traditional method of testing hypotheses. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #601732 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=601732\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> alpha = 0.05<BR>\n" );
document.write( "xbar = 42.5<BR>\n" );
document.write( "s = 5.9<BR>\n" );
document.write( "n = 15<BR>\n" );
document.write( "df = n-1 = 15 - 1 = 14<BR>\n" );
document.write( "We will use the T distribution because n > 30 is not true and we don't know sigma.\r<BR>\n" );
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document.write( "Hypothesis:<BR>\n" );
document.write( "H0: mu = 32.6<BR>\n" );
document.write( "H1: mu =/= 32.6\r<BR>\n" );
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document.write( "Claim is in the null hypothesis H0. This is a two tailed test. The null will be rejected if the test statistic is not between the critical values.\r<BR>\n" );
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document.write( "Test Statistic:<BR>\n" );
document.write( "t = (xbar - mu)/(s/sqrt(n))<BR>\n" );
document.write( "t = (42.5 - 32.6)/(5.9/sqrt(15))<BR>\n" );
document.write( "t = 6.49873476736499<BR>\n" );
document.write( "t = 6.4987\r<BR>\n" );
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document.write( "Critical Values (alpha = 0.05, df = 14)\r<BR>\n" );
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document.write( "Use a table like <a  rel=nofollow HREF=\"http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">this one</a> to find the critical values to be -2.145 and 2.145\r<BR>\n" );
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document.write( "The test statistic 6.4987 is NOT between the critical values -2.145 and 2.145. So we reject the null hypothesis. There is enough statistically significant evidence to reject the null.\r<BR>\n" );
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document.write( "This means that the population mean mu is NOT 32.6. The initial claim is false. <BR>\n" );
document.write( " </SPAN>\n" );
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