Twenty motors are put on an accelerated life test without replacement and the test is truncated after 5 failures. If the first 5 failures occurred at 12.5, 16.8, 24.3, 27.6 and 32.1 hours, assuming an exponential model,

(a) determine a 95% confidence interval for the failure rate of such motors under these accelerated conditions;

(b) test the null hypothesis that the failure rate is 0.005 failures per hour against the alternative that it is less that 0.005 , using the 0.05 level of significance.