According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 53 months. A researcher for a consumer advocate group tests this by selecting 70 bulbs at random. For the bulbs in the sample, the mean lifetime is 52 months. It is known that the population standard deviation of the lifetimes is 4 months. Can we conclude, at the 0.10 level of significance, that the population mean lifetime, , of light bulbs made by this manufacturer differs from 53 months?
Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below.
(a) State the null hypothesis and the alternative hypothesis .
(b) Determine the type of test statistic to use.
(c) Find the value of the test statistic. (Round to three or more decimal places)
(d) Find the two critical values. (Round to three or more decimal places)
(e) Can we conclude that the population mean lifetime of light bulbs made by this manufacturer differs from 53 months?
