According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 42 months. A researcher for a consumer advocate group tests this by selecting 41 bulbs at random. For the bulbs in the sample, the mean lifetime is 39 months. It is known that the population standard deviation of the lifetimes is T months. Assume that the population is normally distributed. Can we conclude, at the 0.01 level of significance, that the population mean lifetime, _|.l, of light bulbs made by this manufacturer differs from 42 months? Per'orm a twotailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places. and round your responses as specied below. (If necessary. consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1. H O H\": _ H 1 (b) Determine the type of test statistic to use. I!' IV |(Choose one) Y | = (c) Finc the value of the test statistic. {Round to three or more decimal places.) (d) Finc the mo critical values. (Round to three or more decimal places.) and (e) Can we conclude that the population mean lifetime of light bulbs made by this manu'acturer differs from 42 months? -SI_IS' Yes '12} No