A manufacturer claims that the mean lifetime, , of its light bulbs is 54 months. The standard deviation of these lifetimes is 6 months. Twelve bulbs are selected at random, and their mean lifetime is found to be 52 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 54 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. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H. H P H : 0 X S P H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 050 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) * 00 0 X (d) Find the p-value. (Round to three or more decimal places.) ? (e) Can we conclude that the mean lifetime of light bulbs made by this manufacturer differs from 54 months? Yes O No