The document presents an interesting problem involving a color TV that was originally set to function for 10,000 hours without any issues. The manufacturers have taken measures to improve this trouble-free time. From the new batch of color TV sets, 100 units have been selected for testing. The average trouble-free time found for these units is 10,150 hours, with a standard deviation of 500 hours. The question posed is whether we can judge that the average trouble-free time of the improved color TV has increased significantly.
This is a statistical problem that requires the use of a five-step hypothesis testing procedure. The significance level (α) for this test is 0.01. The Z values for various significance levels are also provided. For instance, Z0.01 = 2.326. This is a one-tailed test as we are only interested in whether the average trouble-free time has increased, not whether it has decreased.
The problem does not provide an explicit solution but it is a great exercise for those interested in statistics and hypothesis testing. It can help in understanding how to set up and carry out a hypothesis test, and how to interpret the results. This problem could be part of a statistics course or a quality control training program.