Quality control requires that Brito light bulbs have an average life of 1000 hours, with a standard deviation of no more than 20 hours. Each month, a sample of 50 bulbs is tested to see whether current production is meeting the standard. If a statistically significant deviation from 1000 hours mean life is found, the production process must be inspected for faults. In this context, `statistically significant' is taken to mean that the probability that the observed deviation of the sample mean from 1000 is due to chance alone is 10 per cent or less. This month the sample mean life turns out to be 996 hours. What is the probability that this deviation from 1000 is just due to sampling error? Does this sample call for inspection of the production process?
Here you may look at an
answer
to this question--but try it yourself first!