A manufacturer claims that the mean lifetime, μ, of its light bulbs is 45 months. The standard deviation of these lifetimes is 7 months. Thirty-one bulbs are selected at random, and their mean lifetime is found to be 48 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs made by this manufacturer differs from 45 months? Perform a two-tailed test. Then fill in the table below.
Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table
the null hypothesis
the alternative hypothesis
the type of test statistic
the value of the test statistic
the two critical values at the .1 level of significance
(round to at least three decimal places)
can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 50 months