Section 8.2 Summary

1. For a normal population, the distribution of
   

   follows a distribution, with degrees of freedom, where is the sample mean, is the unknown population mean, is the sample standard deviation, and is the sample size. The distribution is symmetric about its mean 0, just like the distribution. However, the distribution is flatter.

2. A confidence interval for is given by the interval
   

   where is the sample mean, is associated with the confidence level and degrees of freedom, is the sample standard deviation, and is the sample size. We can construct a interval whenever either of the following conditions is met: the population is normal, or the sample size is large ().