5.The lifetime of an automobile battery is described by an r.v. \( X \) having normal distribution with unknown mean \( \mu \) hour and known s.d. \( \sigma=150 \) hour. Let \( X_1, X_2, \cdots, X_{25} \) be independent r.v.'s distributed as \( X \) and suppose that \( \bar{x}=1725 \) hour. Test the hypothesis \( H_0: \mu=1800 \) versus \( H_1: \mu<1800 \) at level of significance \( \alpha=0.01 \) and make a conclusion. (10%)