A manufacturer claims that the mean lifetime, mean, of its light bulbs is 52 months. The standard deviation of these lifetimes is 7 months. Ninety bulbs are selected at random, and their mean lifetime is found to be 55 months. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 50 months?

Perform a two-tailed test.

The H0 is mean = 52

The H1 is mean not equal to 52

The type of test is a Z test

The z-statistic is

The p value is ? (rounded to at least 3 decimal places)

Can we conclude that the mean life time average differs from 52 months