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Problem 2-2, Comparing a single mean to a specified value (second example)
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===Section D: Confidence intervals=== To calculate the limits of the confidence interval for the sample mean, we use the following formula: <center><math>\bar{y}</math> confidence interval limits = <math>\mu_0\pm z_{\alpha/2} \sigma/\sqrt{n}</math></center> This tells us the range in which a sample mean could lie in order for us to accept our null hypothesis: <center><math>787.75<\bar{y}<812.25</math></center> We can calculate the confidence interval for <math>\mu_0</math> in a similar way, which tells us the range in which the mean of our theoretical distribution (given a sample mean of 812) could lie in order for us to accept our null hypothesis: <center><math>\mu_0</math> confidence interval limits = <math>\bar{y}\pm z_{\alpha/2} \sigma/\sqrt{n}</math><br /> <math>799.75<\mu_0<824.25</math></center>
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