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Problem 2-2, Comparing a single mean to a specified value (second example)
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===Section C: P-values=== We now calculate a P-value the same way we did in problem 2-1. Graphically, we extend the rejection region inwards from both tails until we run into our z-value. The P-value is the area of the shaded area, calculated in Excel with <tt>=2*NORMSDIST(-ABS(z))</tt> or in R with <tt>2*pnorm(-abs(z))</tt>. These functions integrate a normal distribution from negative infinity to the number we give it (in this case the negative absolute value of z), so we give it our negative z-value and multiply by two in order to get the total area of the shaded regions on the graph. <center>P-value <math>= 0.0549</math></center> Our z-value is very close to the rejection region, so a plot illustrating the extended rejection regions will look nearly identical to Figure 2. <div style="float:left; vertical-align: top">[[Image:2-2fig4.png|thumb|left|'''Figure 4:''' The confidence interval about the sample mean.]]<br> [[Image:2-2fig5.png|thumb|left|'''Figure 5:''' The confidence interval about the theoretical mean.]]</div>
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