A manufacturing process that has been used for many years pr

A manufacturing process that has been used for many years produces light bulbs with a mean life of 1,000 hours and a standard deviation of 100. A new process has been developed. A sample of 36 tubes produced by the new process has a mean of 1,065 hours. The engineers hope that the new process produces bulbs which last longer. Do the new tubes last significantly longer? Use = .01.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   1000  
Ha:    u   >   1000  
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical z, as alpha =    0.01   ,      
alpha =    0.01          
zcrit =    +   2.326347874      
              
Getting the test statistic, as              
              
X = sample mean =    1065          
uo = hypothesized mean =    1000          
n = sample size =    36          
s = standard deviation =    100          
              
Thus, z = (X - uo) * sqrt(n) / s =    3.9          
              
Also, the p value is              
              
p =    4.80963*10^-5          
              
As |z| > 2.326, and P < 0.01, we   REJECT THE NULL HYPOTHESIS.          

Thus, there is significant evidence that the new process produces bulbs which last longer. [CONCLUSION]