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 ten projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the ten machines is given in the table.Could not fit part d and e in the picture but the questions are asking: part d: find the p value and part e: can we conclude that the mean lifetime of light bulbs in infocus projectors, u1, differs from u2, the mean lifetime of light bulbs in proxima projectors? Yes or no

Lifetimes of light bulbs (hours) Infocus 1045, 973, 982, 788, 1186, 944, 999, 605, 871, 682 Proxima 823, 715, 649, 931, 1029, 802, 766, 798, 886, 1056 Send data to calculator v 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, H, 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 H. O p Ho : X S H, : (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.) x 00