A manufacturer of flashlight batteries took a sample of 13 batteries from a day's production and used them continuously until they failed to work. The life as measured by the number of hours until failure was: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562, 298. At the 0.05 level of significance, is there evidence that the mean life of batteries is more than 400 hours? Given: n=13; Ho: μ≤400 hours; Ha: μ>400 hours; decision rule: reject Ho if tc>t(.05, 12) and tc>1.7823 and accept Ho otherwise. Find sample standard deviation, sample mean, tc, decision, and conclusion.