document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201497>Question 1201497</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You wish to test the following claim (Ha) at a significance level of  <BR>\n" );
document.write( "α=0.02.\r<BR>\n" );
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document.write( "Ho:μ=73.2<BR>\n" );
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document.write( "Ha:μ>73.2<BR>\n" );
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document.write( "You believe the population is normally distributed and you know the standard deviation is σ=11.5. You obtain a sample mean of M=78.8for a sample of size  <BR>\n" );
document.write( "n=17.\r<BR>\n" );
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document.write( "What is the test statistic for this sample? (Report answer accurate to three decimal places.)<BR>\n" );
document.write( "test statistic = \r<BR>\n" );
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document.write( "What is the p-value for this sample? (Report answer accurate to four decimal places.)<BR>\n" );
document.write( "p-value = \r<BR>\n" );
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document.write( "The p-value is...\r<BR>\n" );
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document.write( "less than (or equal to) α<BR>\n" );
document.write( "     OR<BR>\n" );
document.write( "greater than α\r<BR>\n" );
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document.write( "This test statistic leads to a decision to...<BR>\n" );
document.write( "reject the null<BR>\n" );
document.write( "     OR<BR>\n" );
document.write( "accept the null<BR>\n" );
document.write( "     OR<BR>\n" );
document.write( "fail to reject the null<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835916 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835916\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> H0 says population mean is equal to 73.2<BR>\n" );
document.write( "Ha says population mean is greater than 73.2<BR>\n" );
document.write( "population mean is 11.5<BR>\n" );
document.write( "sample size is 17<BR>\n" );
document.write( "sample mean is 78.8<BR>\n" );
document.write( "standard error = standard deviation / square root of sample size = 11.5 / sqrt(17) = 2.789159688.<BR>\n" );
document.write( "test z-score = (x - m) / s = (78.8 - 73.2) / 2.789159688 = 2.007773174.<BR>\n" );
document.write( "area to the right of that z-score is equal to .0223336306.<BR>\n" );
document.write( "since the test alpha is greater than the critical alpha, the test is not significant and you conclude that you haven't got enough information to say that the mean is greater than 73.2.<BR>\n" );
document.write( "the test z-score was 2.007773174.<BR>\n" );
document.write( "this was less than the critical z-score of 2.053748911.<BR>\n" );
document.write( "this confirms the p-score results indicating that the test was not significant and that there was not enough information to conclude that the population mean was greater than 73.2.<BR>\n" );
document.write( "here are the results from the calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2023/040605.jpg\"><BR>\n" );
document.write( "for the results to be significant, either the test z-score needs to be greater than the critical z-score, or the test p-value has to be less than the critical p-value.  <BR>\n" );
document.write( "they are consistent with each other.<BR>\n" );
document.write( "if the test z-score is greater than the critical z-score, then the test p-value will be less than the critical p-value.<BR>\n" );
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