12. A university uses an old brand of fluorescent bulb. A manufacturer of a new brand of bulb claims that its new bulb has a longer mean life than the old bulb. The university will switch to this new brand of bulb if it is convinced at the .10 level of significance of the manufacturer's claim. The sample size, sample mean life, and standard deviation for the old and new bulbs are summarized in the table. Will the university switch to the new bulb? (Let u, = the mean life of the old brand and u, = the mean life of the new brand ) Old brand New brand n = 300 1 = 400 X1 = 1200 X2 = 1232.65 S, = 170 S, = 200