document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1169891>Question 1169891</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Find the P - value for the test statistic z=−1.41 for the following null and alternative hypotheses:<BR>\n" );
document.write( "H0: The population mean is 50.<BR>\n" );
document.write( "Ha: The population mean is not equal to 50. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #794741 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=794741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the area to the left of a z-score of -1.41 is equal to .0792698912.<BR>\n" );
document.write( "the critical z-score at the different confidence limits are:<BR>\n" );
document.write( "at 90% = plus or minus 1.645<BR>\n" );
document.write( "at 95% = plus or minus 1.96<BR>\n" );
document.write( "at 99% = plus or minus 2.576\r<BR>\n" );
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document.write( "the alpha is the area in the rejection zone.<BR>\n" );
document.write( "at 90% = .05 on either end<BR>\n" );
document.write( "at 95% = .025 on either end<BR>\n" );
document.write( "at 99% = .005 on either end\r<BR>\n" );
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document.write( "your z-score is within the confidence limits at 90%, 95%, and 99%.<BR>\n" );
document.write( "your test alpha is above the critical alpha limits at 90%, 95%, and 99%.\r<BR>\n" );
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document.write( "your z-score does not support rejection of the null alternative because your statistical results are not significant enough.\r<BR>\n" );
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document.write( "they would be significant if the z-score was above the critical threshold or the alpha was below the critical threshold.\r<BR>\n" );
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document.write( "the critical threshold is set before the test is made.\r<BR>\n" );
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document.write( "there is not enough evidence to support the alternative hypothesis that the mean is not equal to 50.\r<BR>\n" );
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document.write( "the tester is the one who sets the confidence limits.<BR>\n" );
document.write( "in order for your test to pass the critical threshold, the critical z-score would have had to be less than plus or minus 1.41 and your critical alpha would have had to be more than .0792698912.\r<BR>\n" );
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document.write( "that would have required a two tailed confidence level of .841460173 or less.\r<BR>\n" );
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document.write( "while there's nothing to stop the tester from setting a confidence limit so low,  it's not typically done.\r<BR>\n" );
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document.write( "the higher the confidence limit, the greater the confidence that the results are valid.\r<BR>\n" );
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document.write( "here's a reference on critical z-scores and alphas.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.statisticshowto.com/probability-and-statistics/find-critical-values/\" target = \"_blank\">https://www.statisticshowto.com/probability-and-statistics/find-critical-values/</a>\r<BR>\n" );
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document.write( "here's a reference on confidence limits.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.statisticshowto.com/probability-and-statistics/confidence-interval/\" target = \"_blank\">https://www.statisticshowto.com/probability-and-statistics/confidence-interval/</a>\r<BR>\n" );
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