Chapter 6.4, Problem 6Q

Suppose $n=36$ observations are taken from a normal distribution where $\sigma =8.0$ for the purpose of testing $H_0:\mu =60$ versus $H_1:\mu \ne 60$ at the $\alpha =0.07$ level of significance. The lead investigator skipped statistics class the day decision rules were being discussed and intends to reject $H_0$ if $\bar{y}$ falls in the region $\left(60-{\bar{y}}^{\ast },60+{\bar{y}}^{\ast }\right)$.

• (a) Find ${\bar{y}}^{\ast }$.

• (b) What is the power of the test when $\mu =62$?

• (c) What would the power of the test be when $\mu =62$ if the critical region had been defined the correct way?