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 Summation(x-1000) = 1890 and Summation(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% sigicance level, show that there are no grounds to dispute this claim.

Okay so if I perform the test, I'll have

H_0: mu = 1200

H_a: mu < 1200 (< sign since I want to dispute his claim?)

However, I recall the values for the sample mean and sample standard deviation or sample variance. How do I get these values? Obviously, I feel like the summation parts given in the question above gives me certain information but I'm not really sure what to do with them.

Please advise. Also, please excuse me for not knowing how to type out the summation symbol.