A purchasing manager for a large university is investigating which brand of LCD projector to purchase to equip their classrooms. Of major concern is thelongevity of the light bulbs used in the projectors. The purchasing manager has narrowed down the choice of projector to two brands, Infocus and Proxima, andwishes 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 oneach of the twelve projectors is given in the table.Lifetimes of light bulbs (hours)Infocus 783, 938, 876, 844, 748, 779, 790, 1116, 895, 1001, 1106, 1064Proxima 929, 783, 615, 871, 739, 960, 887, 782, 1020, 754, 649, 787Send data to calculatorSend data to ExcelAssume 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 u, the mean lifetime of light bulbs in Infocus projectors, differs from u, the mean lifetime of light bulbsin 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 offormulas.) (a) State the null hypothesis H, and the alternative hypothesis H1.H, :0H :0(b) Determine the type of test statistic to use.(Choose one)OSOO20(c) Find the value of the test statistic. (Round to three or more decimal places.)O

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(a) State the null hypothesis H, and the alternative hypothesis H1. H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) OSO O20 (c) Find the value of the test statistic. (Round to three or more decimal places.) O