6.114 Sample size determination.

Example 6.26 (page 343) considers the test of $H_0:\mu =473$ against $H_a:\mu \ne 473$, where $\mu$ is the mean fill amount. The population standard deviation is given to be $\sigma =2$. Suppose that the testing is performed at a 5% significance level. Without use of software, determine the sample size that is minimally required to give at least 0.8 power.