Duracell batteries claim that their AA size batteries have an average life longer than 15 hours*. A sample of 9 mechanical boxing kangaroos is tested using the Duracell batteries with the following life times recorded in hours:

16.5

14.8

15.3

16.8

14.8

14.6

15.9

16.1

14.7

It is known from past test records that the lifetime of Duracell AA battery is normally distributed with a standard deviation (s) of 0.6 hour. Based on the above information, test Duracell’s claim allowing for a probability of a Type I error of 1% using:

(a)    the p-value approach, and,(b)   the critical value approach