A manufacturer claims that the mean lifetime of the light bulbs he produces is at least 1200 hours. A random sample of 10 bulbs is taken and the lifetimes are observed. The results are summarized by ? (x ? 1000) = 1890 and ?(x ? 1000)2 = 362050.2, where x is measured in hours. Assuming the lifetimes of the bulbs to be normally distributed, and using a 5% sigificance level, show that there are no grounds to dispute this claim.