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