(Solved): According to a report done by 58 . J Power, the mean lifetime of the tight bulos it manufactures is ...

According to a report done by 58 . J Power, the mean lifetime of the tight bulos it manufactures is 50 months. A researcher for a consumer advocate group tests. this by selecting 70 butbs at random. For the butbs in the sampie, the mean tifetime is 51 monthis. It is known that the population standard devation of the lifetimes is 5 months, Can we conclude, at the 0.01 level of significance, that the population mean lifetume, $?$, of light bulbs made by this manufacturer differs from 50 months? Perform a two-talled test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis $H_0$ and the alternative hypothesis $H_1$. $\begin{array}{l}{H}_0=?\\ H_1=?\end{array}$ (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the $p$-value. (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 50 months? Yes No