A manufacturer of flashlight batteries claims that the average life of her batteries is larger than 400 hours. Peter, as a quality assurance officer in the manufacturing company, took a random sample of 13 batteries from a day's production and used them continuously until they failed to work. The lifetime (hours) until failure was: 342 426 317 545 264 451 1049 631 512 266 492 562 298

(a) At the 0.05 level of significance, is there evidence that the manufacturer's claim is correct?

(b) What is the p-value?