BIG Corporation advertises that its light bulbs have a mean lifetime, , of 3000 hours. Suppose that we have reason to doubt this claim and decide to do a statistical test of the claim. We choose a random sample of light bulbs manufactured by BIG and find that the mean lifetime for this sample is 2800 hours and that the sample standard deviation of the lifetimes is 600 hours. Based on this information, answer the questions below.

What are the null hypothesis () and the alternative hypothesis () that should be used for the test?

: is
?

?

: is
?

?

In the context of this test, what is a Type I error?

A Type I error is
?
the hypothesis that is
?

?
when, in fact, is
?

?
.

Suppose that we decide not to reject the null hypothesis. What sort of error might we be making?
?