document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201121>Question 1201121</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with mean I.Q 100 and standard deviation 12? (Test at 5% level of significance) </SPAN>\n" );
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document.write( "Population info<BR>\n" );
document.write( "mu = population mean = 100<BR>\n" );
document.write( "sigma = population standard deviation = 12\r<BR>\n" );
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document.write( "Hypothesis:<BR>\n" );
document.write( "Null: mu = 100<BR>\n" );
document.write( "Alternative: mu =/= 100<BR>\n" );
document.write( "The \"not equals\" in the alternative hypothesis indicates we'll be doing a two-tailed test.\r<BR>\n" );
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document.write( "Sample info<BR>\n" );
document.write( "xbar = sample mean = 99<BR>\n" );
document.write( "n = sample size = 1600\r<BR>\n" );
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document.write( "Compute the test statistic<BR>\n" );
document.write( "z = (xbar - mu)/(sigma/sqrt(n))<BR>\n" );
document.write( "z = (99 - 100)/(12/sqrt(1600))<BR>\n" );
document.write( "z = -3.33 approximately\r<BR>\n" );
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document.write( "Use a Z table such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.ztable.net/\">https://www.ztable.net/</a><BR>\n" );
document.write( "to find that<BR>\n" );
document.write( "P(Z < -3.33) = 0.00043<BR>\n" );
document.write( "This is the approximate area under the standard normal curve to the left of z = -3.33<BR>\n" );
document.write( "We're doing a two-tailed test, so we double this area value.<BR>\n" );
document.write( "2*0.00043 = 0.00086 <BR>\n" );
document.write( "This is the approximate p-value.\r<BR>\n" );
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document.write( "The p-value 0.00086 is smaller than alpha = 0.05, so we reject the null.\r<BR>\n" );
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document.write( "We conclude that the sample of 1600 children having a sample mean IQ of 99 very likely could not have been drawn from a population with mean IQ 100 and standard deviation 12.<BR>\n" );
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