The quality control manager at a cell phone battery factory

The quality control manager at a cell phone battery factory needs to determine whether the mean life of a large shipment of batteries is equal to the specified value of 375 hours. The process standard deviation is known to be 100 hours. A random sample of 64 batteries indicates a sample mean of 350 hours. How much evidence do we have that the shipment is meeting the specified value?

A.No evidence

B. Some evidence

C. Strong evidence

D. Very Strong evidence

E. Extremely Strong evidence

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   375  
Ha:    u   =/=   375  
              
As we can see, this is a    2   tailed test.      
                          
Getting the test statistic, as              
              
X = sample mean =    350          
uo = hypothesized mean =    375          
n = sample size =    64          
s = standard deviation =    100          
              
Thus, z = (X - uo) * sqrt(n) / s =    -2          
              
Also, the p value is              
              
p =    0.045500264          
              

Please refer to your convention in close as to in which category this p value falls. It seems your class agreed to a certain standard for p values.