document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196778>Question 1196778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Question # 8: Review Part 2: Hypothesis Testing: Find test statistic and p-value and make conclusion for a mean (using T-Test).\r<BR>\n" );
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document.write( "x= 137\r<BR>\n" );
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document.write( "s = 14.2\r<BR>\n" );
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document.write( "n = 20\r<BR>\n" );
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document.write( "Ho: μ = 132\r<BR>\n" );
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document.write( "H subscript A colon space mu not equal to 132\r<BR>\n" );
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document.write( "α = 0.1\r<BR>\n" );
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document.write( "Test statistic: t = 1.57\r<BR>\n" );
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document.write( "p-value = 0.1318\r<BR>\n" );
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document.write( "Reject Ho in favor of HA\r<BR>\n" );
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document.write( "There is enough evidence to show that the mean is significantly different from 132.\r<BR>\n" );
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document.write( "	<BR>\n" );
document.write( "Test statistic: t = 1.57\r<BR>\n" );
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document.write( "p-value = 0.1318\r<BR>\n" );
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document.write( "Fail to reject Ho \r<BR>\n" );
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document.write( "There is not enough evidence to show that the mean is significantly different from 132.\r<BR>\n" );
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document.write( "	<BR>\n" );
document.write( "Test statistic: t = 1.57\r<BR>\n" );
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document.write( "p-value = 0.0582\r<BR>\n" );
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document.write( "Reject Ho in favor of HA\r<BR>\n" );
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document.write( "There is enough evidence to show that the mean is significantly different from 132.\r<BR>\n" );
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document.write( "	<BR>\n" );
document.write( "Test statistic: t = 1.57\r<BR>\n" );
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document.write( "p-value = 0.0582\r<BR>\n" );
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document.write( "Fail to reject Ho \r<BR>\n" );
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document.write( "There is not enough evidence to show that the mean is significantly different from 132. </SPAN>\n" );
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document.write( "Given info:<BR>\n" );
document.write( "xbar = 137<BR>\n" );
document.write( "s = 14.2<BR>\n" );
document.write( "n = 20<BR>\n" );
document.write( "alpha = 0.1\r<BR>\n" );
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document.write( "Null Hypothesis: mu = 132<BR>\n" );
document.write( "Alternative Hypothesis: mu =/= 132<BR>\n" );
document.write( "This is a two-tailed test because of the \"not equal\" sign in the alternative hypothesis.\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 = (137 - 132)/(14.2/sqrt(20))<BR>\n" );
document.write( "t = 1.57469575880267<BR>\n" );
document.write( "t = 1.57\r<BR>\n" );
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document.write( "Use technology to compute the p-value. There are many methods that it would take a while to go over them all, but here's one free online calculator you can use<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.statology.org/t-score-p-value-calculator/\">https://www.statology.org/t-score-p-value-calculator/</a><BR>\n" );
document.write( "Type in 1.57 as the t score and 19 as the degrees of freedom (since df = n-1 = 20-1 = 19)<BR>\n" );
document.write( "We're doing a two-tailed test.<BR>\n" );
document.write( "Don't worry about the significance level since all we care about is the p-value.\r<BR>\n" );
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document.write( "You should get a p-value of roughly 0.1329 from this two-tailed test.<BR>\n" );
document.write( "I'm curious to know where your teacher is getting 0.1318 from, but this might be from a reference table of some sort.\r<BR>\n" );
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document.write( "Rule: if p-value is smaller than alpha, then reject the null. \r<BR>\n" );
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document.write( "Since the p-value is not smaller than alpha, this means we fail to reject the null.<BR>\n" );
document.write( "There isn't enough evidence to overturn it. <BR>\n" );
document.write( "We don't have enough evidence to show the mean is significantly different from 132.<BR>\n" );
document.write( "So for now we conclude that mu = 132 is the case.\r<BR>\n" );
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document.write( "<font color=red>Answer: Choice B</font><BR>\n" );
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