A purchasing manager for a large university Is Imestigating which brand of LCD projector to purchase to equip their castrooms. Of major concem 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 Illetime of the bulbs used. The purchasing manager obtained thirteen projectors of each brand for testing over the last several academic terms. The number of hours the bulbs lasted on each of the thirteen projectors is olven in the table. 1 Lifetimes of light bulbs (hours] Infocus 789 1081 773 1016 849 968 889 767, 942, 821 868, 924 825 Fromima 859, 667, 764 769 746 767, 1096 946 878 962 733 702 829 Send data to calculator Send data to Excel Assume that the two populdons of lifetimes are normally distributed and that the population varlances are equal Bon we conclude, at the 0.05 level of significance, that i , the mean lifeume of light bulbs in Infocus projectors, differs from po, the mean lifetime of light bulbs 1 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, {U necessary, consult a list of (a) State the null hypothesis , and the alternative hypothesis H, H. D H D [bj Determine the type of test statistic to use. Degrees of freedom: Ul C) Find the value is the best statistic. ( Round to three or more bedmal places.] 16 (d) Find the two critten ivalues at the 0.05level of significance. (Round to three of more decimal places. Can we conduce that II , the mean lifetime of light bulbs in Infocus projectors, afters from lly, the mean lifetime of light bulbs in Proxima projectors