According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is $1 months. A researcher for a consumer advocate group tests this by selecting 23 bulbs at random. For the bulbs in the sample, the mean lifetime is 53 months. It is known that the population standard deviation of the lifetimes is 9 months. Assume that the population is normally distributed. Can we conclude, at the 0.05 level of significance, that the population mean lifetime, u, of light bulbs made by this manufacturer differs from 51 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,. P Ho : 0 X S p H :0 (b) Determine the type of test statistic to use. (Choose one) 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 070 00(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 51 months? OYes ONo