A manufacturer claims that the mean lifetime, , of its light bulbs is months. The standard deviation of these lifetimes is months. Forty bulbs are selected at random, and their mean lifetime is found to be months. Assume that the population is normally distributed. Can we conclude, at the level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from months?

Perform a two-tailed test. Then fill in the table below.

null hyoothesis: ?????

alternative hypothesis: ?????

using z test find

value of test statistic: ?????/

the p value: ??????

can we conclude that mean lifetime of bulbs made form this manufacturer differs from 46 months?