A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip "smart" classrooms. Of major concern is the longevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and Proxima, and wishes to determine if there is any difference between the two brands in the mean lifetime of the bulbs used. The purchasing manager obtained nine projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the nine machines is given in the table. Lifetimes of light bulbs (hours) Infocus 1065, 946, 821, 785, 895, 853, 845, 895, 678 Proxima 860, 522, 1026, 887, 921, 814, 1167, 600, 806 Send data to calculator Send data to Excel Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can we conclude, at the 0.05 level of significance, that the mean lifetime of light bulbs in Infocus projectors, , differs from My, the mean lifetime of light bulbs in Proxima projectors? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H1. P Ho : 0 S P H, : 0 (b) Determine the type of test statistic to use. (Choose one) OSO 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0*0 00 X 5 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we conclude that the mean lifetime of light bulbs in Infocus projectors, My, differs from My, the mean lifetime of light bulbs in Proxima projectors? OYes ONo