In a non-replacement life test, 50 water turbines were put into continuous operation, and the first 3 failures occurred after 400,600, and 1,050 hours.

(a) Assuming the exponential model, construct an \(85 \%\) confidence interval for the mean life of this kind of water turbines.

(b) To check the manufacturer's claim that the mean life of these turbines is greater than 7,500 hours, test the null hypothesis \(\mu=7,500\) against an appropriate alternative, so that the burden of proof is put on the manufacturer. Use \(\alpha=0.005\).