The Quality Control Manager of a Major Cell Phone Provider $\alpha$

The quality control manager of a major cell phone provider is concerned about the life of the cell phone batteries they use.He took a sample of 13 batteries from a recent shipment and used them continuously until they failed to work.The manager measured the number of hours the batteries lasted and found the mean to be 550.4 with a standard deviation of 315.3.What is the critical value for $\alpha$ = .10 to test the claim that the mean life of the batteries is more than 400 hours.

A) -1.356
B) 1.356
C) 1.282
D) 1.782
E) -1.782