LIFE TESTS FOR ENERGY-SAVING LIGHT BULBS

To characterize the lifetime of a new brand of energy-saving light bulbs, a sample of 10 were tested in a specially designed facility  where they could be left on continuously and monitored electronically to record the precise number of hours until burn out. The experimental design calls for halting the test immediately after 8 of the 10 light bulbs have burned out. The result, in thousands of hours, arranged in increasing order is as follows:

(1.599, 3.380, 5.068, 8.478, 8.759, 9.256, 11.475, 14.382)

i.e., the ?rst light bulb to burn out did so after 1,599 hours, the next after 3,380 hours, and the 8th and ?nal one after 14,382 hours. Obtain an estimate of the mean lifetime and test the hypothesis that it is 12,000 hours against the alternative that it is  not.