To investigate the average time to failure of a certain soldered object subject to continuous flow of current, 5 soldered objects were subjected to specified volts and amperes of current and their times to failure were 426, 589,694,810 and 1,100 circuits of current.

(a) Assuming the exponential model, construct a 90% confidence interval for the mean life (in thousands) of circuits of such a solder under the given current flow conditions.

(b) Assuming the exponential model, test the null hypothesis that the mean life of the solder under the given current flow conditions is 1 million circuits against the two-sided alternative \(\mu eq 1\) million. Use the level of significance 0.05 .