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 twelve projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the twelve machines is given in the table. Lifetimes of light bulbs (hours) Infocus 502, 856, 988, 884, 857, 831, 763, 919, 787, 1067, 806, 1144 Proxima 685, 937, 785, 760, 716, 869, 845, 748, 755, 949, 899, 759 Send data to calculator v Assume that the two populations of lifetimes are normally distributed and that the population variances are equal. Can we conclude, at the 0.01 level of significance, that there is a difference in the mean lifetime of the light bulbs in the two brands? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)