Duracell

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

 :  = 15

 :  > 15

 =  = 15.5

 = 0.6

Population mean,  = 15

Sample mean,  = 15.5

Standard deviation,  = 0.6

P (> 15) =P 

                = P 

               = P 

               = 0.00621

Since the calculated p-value=0.00621 is less than significance level (0.01), we reject null hypothesis and justify the claim that an average of life of Duracell AA is longer than 15 hours.

(b)The critical value approach

 :  = 15

 :  > 15

 =  = 15.5

 = 0.6

Population mean,  = 15

Sample mean,  = 15.5

Standard deviation,  = 0.6

P (> 15) =P 

                = P 

               = P 

Critical value at 0.01 =2.326 (from standard normal table)

Since the calculated Z = 2.5, which is greater than critical value (2.326), we reject null hypothesis and justify the claim that an average of life of Duracell AA is longer than 15 hours.